One of my daughters is like this (now in her 40s) and a few years ago my sister suggested to her that she allowed us to take photos on condition that she had the right to delete them from the camera if she wanted to. Three cheers for digital cameras.
This has helped a lot as now the photos we do take are no longer smudges and smears as she turns or ducks out of sight, and she no longer pulls faces at the camera or puts her hand in front of her face. It also means that we can now take lots of photos of her at family events because she's no longer hiding in the loo or kitchen when the cameras are out, and there is nearly always one or two that she lets us keep. After all, this is what professional photographers do; they takes hundreds to get the one or two that are right.
For your particular situation, if it's the whole of you that you don't like being photographed, then make sure you stand in a middle or back row. Wear a large hat to conceal some of your face or at least put it in shadow? In this sort of group photo each person's face is usually pretty tiny anyway. Don't look directly at the camera, try a half way between full face and profile, then you can pretend it's not there. And don't get a copy of the photo if you are convinced that you being in it has spoilt it.
Finally, don't expect a photo to look like you! We only see our own face in mirrors and faces are not symmetrical. You can prove this by putting a mirror down the middle of any photograph so you see one half reflected as a mirror image. The two halves reflected give two completely different faces. If you rarely have a photo taken of yourself, then you are not used to seeing yourself as others (and the camera) see you which is why you think you don't look right.