Don't feel bad at all! in my (measly) year and a half, I have done two completley stupid things. I ate a chicken sandwhich. (I was eating a plate of egg sandwhiches, and didn't realise there were none left, picked up another, took a bite, chewed it for about 5 secconds, realised what it was, ran to the bin, practically scooped my mouth out of gunk, then went and took a half an hour shower, and brushed my teeth twice.)
I also bought a pastie. I asked the evil *censored* at the canteen for something that was suitable for vegetarians, she told me that there was a veggie pastie, throughout eating it i kept comming across small pieces of meat. I kept asking my friend (who is not vegetarian, and works in a cafe that serves this sort of stuff) if he thought it was meat, he kept telling me that it couldn't be, that it was potato, and it was ok to eat, because the canteen *censored* wouldn't sell me something that wasn't vegetarian if i'd asked for vegetarian. It wasn't till i'd gotton to the end (of my 5 dollar rip off pastie, that would have cost about 50 cents to produce), when i found a HUGE chunk of meat, I"m talking a whole pigs leg worth of meat (not realy, but ya know. to me it was huge.) and then i felt sick, and nearly threw up.
So don't worry about it. One tiny little bit of animal isn't going to kill you. Being veg isn't about scrutinising every piece of food you ever eat, down to the 'this was in the same air as a meat eater', it's about showing other people that animals deserve respect and rights, that animal slaughter is inhumane, and that farmers care about profits, not animals. If you accidentally eat something, spit it out, exclaim how bad it tasted. (the chicken tasted like slimy gross gunk), and how glad you are that you didn't eat that discusting carcase for tea. Show people that you're not a perfectionist (even if you are), and that you are a normal, happy human being. It's ok to laugh at your mistakes, everyone makes them. Even the most perfect animal lover in the world, so don't take it harshly at all.