You talk about things not making sense, but pretty much everything you've proposed doesn't make sense. And you certainly *could* have alternative explanations for flight not involving wings, which wouldn't work unless your body structure fundamentally changed as well.
Some options that would make more sense than wings might involve having the ability to produce and store within your body an absurdly lightweight gas or chemical.
That would depend entirely on the form of teleportation. If you were bending time and space to link two locations where you'd see the exit point, none of those factors would apply. Unpredictable teleportation is generally a lazy limiting trope.
Dood, did people ever tell you you're fun at parties?