Sneak Attack Does Work While Flanking
What in the world is your DM basing this ruling on? The rules are very clear on this.
The rogue’s attack deals extra damage any time her target would be
denied a Dexterity bonus to AC (whether the target actually has a
Dexterity bonus or not), or when the rogue flanks her target.
Go Ask The DM Again. It's entirely possible he just misunderstands the rules.
If He Doesn't Misunderstand The Rules
If this is a deliberate house rule for some reason I can't possibly fathom, then you should ask for a retcon and totally redo your character, making it into something else. Rogues aren't a super strong class in the first place. Take away sneak attack and a dual wielding Rogue is really weak in combat. You could try to switch to ranged, but you've already wasted a feat on two weapon fighting that you can't get back, and ranged combat is pretty feat intensive.
Even then, ranged combat will still be really weak. With the sneak attack ruling, you will only be able to use it more than once if you've got greater invisibility, or you can stealth after attacking with Hide (which is taken at a -20 on your roll, so it's basically impossible at low level). You'll just be doing bow damage, which is really lame.
If he says that you must play a Rogue and he won't undo his house rule, then I'd just deliberately get killed. Nobody can afford a resurrection at low level, so you can make something else. If he tries to still force you to play a Rogue despite his wonky ruling, quit the campaign. It's not worth the frustration when DMs try to railroad players like that, and I say that as someone currently DMing a two years and running campaign.
If the DM really wants a Rogue in the party, he should not change the rules to make it weaker. Rogues are already not one of the stronger classes in the game, and a ruling like this is really damaging.
On House Rules & Misunderstandings
If this is a misunderstanding on the DM's part of the rules, okay. That happens. If you point out the rules and he corrects the mistake? No problem. I've been running a campaign for years and occasionally I get corrected by my players. :)
If not... you have to ask yourself if you want to stay in a game like this. This kind of seemingly random house ruling that severely harms the effectiveness of a player is a good way to create a toxic environment at the table. The next time someone gets surprised like this, what happens? What if it causes a character death? I've seen that type of thing before, and it ended a campaign.
Consistency in rulings is important from a DM. If he has house rules that affect player effectiveness, he needs to spell those out before you run into them. Allowing you to make a Rogue without warning you how badly he'd weakened it beforehand is not something a responsible DM does, and if he's okay with doing that, you run a very real risk that he'll just do it again in the future. You have to decide if you're alright with being in a game where that's a thing.
At it's base, Rogue stealth isn't that good. Hide as a skill is very limited in when you can use it, and a lot of powerful creatures have spot checks and special senses so high that it's just not going to help you when you really need it. It's largely totally unworkable in combat for sneak attack purposes.
It can be used to good effect, but it requires getting things like Hide In Plain Sight, or get Invisibility (or the truly awesome Greater Invisibility). But you need prestige classes, items, or a spellcaster party member buffing you to get those things.
Hide is handy when scouting, especially if paired with Darkvision (so you can see without a light source), and in a town setting where you can use it a lot. For combat, Hide is a very poor method of stealth that won't actually do much for you.
Do You Need A Rogue?
It's pretty rare that a party actually needs a Rogue. Are they helpful? Absolutely! My wife is playing one right now, and she seaches for loot, finds the traps, disarms the traps, and laughs at enemies that try to hit her with fireballs. If the Wizard casts greater invisibility on her, she also goes to town and deals big time damage. (And I mean big time, 6 attacks with 6d6 sneak attack dice is really nasty.)
The thing is that there are several ways to get trapfinding (outside of core, core only it's a lot harder). Once you know the trap is there, it can be disarmed lots of ways, including just having someone set it off (summoned monsters are great for this). Locks can be magically opened or smashed through. Other classes can do the "party face" social role just as well.
If you can't get trapfinding, then you have the Barbarian open the door, or send in the animal companion first. I've rarely seen a campaign where traps were so lethal that trapfinding was absolutely essential, and if your DM tries to run one when nobody has trapfinding, he'll soon find himself dealing with a party wipe.
So, you should play a Rogue if you like the class and want to play it. You should not play one out of a sense that they're required. They are not. There are other ways to do almost everything in 3.5.
If I Were In Your Shoes
I'd quit. Your DM might not think it's a big deal, but IMO he has no idea what he's doing if he is changing sneak attack so drastically. He's pretty much destroyed it as a functional ability until you get access to Greater Invisibility, which will be a very long time from now (if a party member will cast it on you, even longer if you have to get it through a wand or something). You will never be competitive in damage with these rules, and as a class with low survivability as well, you'll likely find combat somewhat less than fun.
It's not worth it. I want to have fun when I play, not sit around doing next to nothing most of the night hoping that a trap comes up at some point, especially when the problem only exists because of an absurd house rule.
It's also a friendship risk. If the DM is your friend and you're not having fun in his game due to this, that will risk bleeding into the friendship. Not playing at all is safer.