A Ranger Beast Master could choose a Pteranodon as an animal companion
The PHB states:
At 3rd level, you gain a beast companion that accompanies you on your adventures and is trained to fight alongside you. Choose a beast that is no larger than Medium and that has a challenge rating of 1/4 or lower.
Pteranodon's are medium sized beasts of challenge rating 1/4 so, by the rules they are a legal choice for a beast companion.
When you asked if this was 'acceptable', if you meant something other than 'is it allowed by the rules' I suggest you are best discussing that with your DM. Maybe there are no dinosaurs in their gameworld? If that's the case there is another option for a beast companion with a fly speed - a Blood Hawk. As a small beast it's base damage roll is less impressive than a Pteranodon's but, depending on your playstyle, Pack Tactics and Keen Sight could prove very useful.
In your situation, it's unlikely to have a bad effect on game balance
Will it be fun for the rest of the party? I can't say for definite - you know your group better than I do.
However, the most common balance complaint (or the most exploitable feature) about allowing a Pteranodon as a beast companion is that small races can use them as a flying mount. If your DM and your party are both already happy with you playing an Aarakocra, and thus having a flying speed of your own, having a flying beast companion is less likely to be an issue. When it flies, your Pteranodon won't be doing anything your character can't already do without it.
Flyby is a pretty powerful ability that increases your pteranodon's survivability considerably - however, a well timed Pounce from a Panther can swing an encounter, and a Wolf, with Pack Tactics, should be attacking with advantage most of the time. With that in mind I don't think Flyby is a gamebreaking.
More generally, Ranger Beast Master's are widely considered to be one the more underpowered class archetypes. So, even if choosing a Pteranodon as your beast companion boosts your power level a little bit, relative to the rest of the party, that's probably not a bad thing.