Since I started DMing D&D a long, long time ago, I found that the dynamics of a mixed group of male ande female players is a tad different from a one-sex only group of players. This is purely anecdotal, however, and fruit of my own experiences and by no means is representative of the general gamer population.
Note that, for the purposes of the following text, the DM is not considered a player. All of those observations were made from a male DM point of view. Also, on Brazil, sexism in game-related matters is almost non-existent, so we DMs have usually one less problem to deal with.
Onwards to my experiences!
1) All-female and all-male groups are completely different beasts.
When you DM to an all-male group, often the group takes the more common adventure, action-oriented group with some roleplay sprinkled here and there. While individually they may show interest in romance or drama-oriented games, as a group they tend to prefer the classical D&D experience. Male players also tend to be more individualistic but not outright selfish. All-female groups show more cohesive, group-oriented behavior and they show a preference for more acting instead of more action. Their roleplay is usually deeper and they tend to avoid more fights than their male counterparts. They don't necessarily seek for romance oriented games but they don't avoid it either - if it shows up on the board, they tend to embrace it more gracefully than their male counterparts.
2) Groups where only one player is from a different gender are most of the time indistinguishable from a one-gender only group when sexist behavior is absent.
When you have a single female on a male-dominated group, the female player normally conforms and behaves just as "one of the guys". You don't usually notice flirting on the table, but when it happens it is between a single couple of players, not in a more generalized manner as described on the OP. Females in this setting take on noticeably more masculine behaviors while in group - even the way they tend to sit changes a bit, with a more comfortable, laid-back posture. You can also observe them openly burping, making typical dirty jokes that males normally are famous for, and other plethora of male-associated behaviors.
When the situation is reversed - a single male in a female-dominated group - the opposite situation happens and that lonely guy becomes "one of the girls" and the experience ends up the same as a female-players-only group. Even usually macho-mode guys end up accepting "girly stuff" in this group setting - they tend to behave in a more polite and educated way, rarely do dirty jokes, and even enroll on more female-oriented roles in-game, such as maternity or romantic drama. I also noticed that a single guy in a female-dominated group is more open to experiment more feminine stuff - like hot-pink nail polish, acne creams, and even a bit of makeup - when presented the option by their female peers. I saw this happen four times already with four different male players, so I don't think it was a specific characteristic of a single player.
3) Two female players in a male-dominated group or two male players in a female-dominated group creates more tension than more mixed or more homogeneous groups.
There is an interesting effect that appears to happen when you have a group with two people of the a given gender together with three or more people of the other gender. I'm not sure why this happens, but the change in group dynamics is evident. This is something I call "queen-bee effect". It happens almost the same way for two guys in a group of females or two females in a group of guys, but the females-in-group-of-guys is way more noticeable.
When you have a setting like this one, the two players of the gender that is under-represented at the table almost always start to compete with each other for dominance. They tend to be increasingly flirtatious (females) or chivalrous (males) regarding the players of the other gender and start to push forward their ideas while putting away the ideas of their "rival". They also seem to become way more stressed out during gaming, focusing more on competing with their rival than enjoying the game by itself. This effect is somewhat harmless in males-in-female-group but can be really disruptive in a female-in-male-group.
A player sometimes enters what I call the "Queen-bee Mode", in which they try "rule" over the table and be the only player of a given gender that gets the other gender attention. Females in queen-bee mode are usually more provocative, flirtatious, and back-stabbing than they are in other group settings, while males tend to be more assertive, chivalrous, and aggressive.
What you are experiencing sounds somewhat like this - this new player is acting like a queen-bee, trying to get the male attention for herself while reducing the other female on the table (you) to a "worker drone" state. When she reinforces her sexuality, she becomes the female symbol for the group, putting a shadow over the fact that you are also a female. I'm not sure from where this behavior comes, but that usually means that she is jealous of you, not the other way around.
The queen-bee effect is especially present in LARPS.
4) Mixed groups with at least three players from each gender are way more manageable than the group setting presented in my observation #3
More mixed groups with somewhat equally represented genders tend to behave way better than a group with a underrepresented gender. In those settings, while the Queen-bee effect may exist, it is rarer and less significant. This group setting is normally more balanced and more friendly. You will probably end up with two players in the leading position of the group, one for each gender. While one of them will be the "official group leader", the other one will have as much influence as the first one, even if it is not recognized. Think about how your father and mother behaved at your home - most of time, while the father seemed like "the head" of the family, the mother had as much power (if not more!) than him during the decision making. Sure, it was an indirect, more subtle decision power, but it was power anyways.
From what I could observe, there are actually two groups in this setting: a "female group" and a "male group". Those two groups, while working together and pushing forward towards the goal of the adventure, seem to pack up differently while making decisions both out and inside the game. Normally, the male lead-player will give a suggestion and will be backed up by the other male players, while being confronted by the female leader which is in turn backed up by the other female players. In a sense, this setting seems more like DMing to two homogeneous groups that happen to work together instead of a single, heterogeneous supergroup. As time passes, however, the groups will mingle up and become more cohesive, more intense friendships will develop, and you'll end up with a healthy, diverse group of friends.
Heck, you may even end up forming real-life romantic couples with a setting like this. For some reason, role-playing being in love with someone can sometimes have a weird reflection on real-life and you end up actually being in love with someone.
Well, that's how I ended marrying my SO, at least!
The Bottom Line and What You Should Do
You can do two things, in this situation, but first you need to understand why she is doing what she is doing. She probably doesn't even realize that what she is doing isn't really nice to you. So, my first recommendation is to talk to her. Not to discuss this and ask her to change, but in a friendly, open way. Even giggle a bit while talking to her. Put her behavior on the spot, but in a lighter tone. Comment about how it is funny, some of the jokes and all, but tell her that you are not used to it and sometimes feel uncomfortable. Always keep the light tone, however. Show her that this behavior of hers is making you feel vulnerable, and a bit alienated. Approach her as a fellow human and as a potential friend. Try to change a bit of the rivalry she has with you to friendship. If she understands that you - her potential new friend - is feeling a bit bad because the way she behaves, she may very well tone it down a bit. Don't expect it to disappear - she's a queen-bee after all - but it may very well become way more manageable.
Failing that, open yourself to your DM. Tell him that she is making you uncomfortable but you want to keep playing with them, make the suggestion to start a second group without her, on a different schedule. It may even be just you, another player and the DM, or even you and the DM.
He may very well accept that - smaller groups are easier to manage and you can create deeper, more interesting tales that way.