You only felt sick. No problem. On my third lesson I threw up all over my instructor!!! Needless to say, he wasn't amused - though he did hide his annoyance quite well.
Things got better, and I ended up flying long distances in both f/w aircraft and helicopters, and instructing in the latter. Oh, and doing helicopter flight test articles for magazines, which sometimes involved throwing them around. I never got to like the throwing around stuff; I always got a little queasy, though it was manageable. But 'normal' flying - no problems.
You've been given good advice so far. I agree with all of it, but as an ex-instructor I would emphasise...tell your instructor! He'll fly you more gently, and also make sure he has a supply of sick bags for emergencies. It's nothing to be ashamed of; it's extremely common. And it will probably go away, or at least get a lot better.
Just one more thought... It's never happened to you before, in any form of transport? Perhaps you were just having a bad day, a minor stomach upset, or similar. Maybe you're worrying too much here.