You should really try to focus on your body and why it is happening. It sounds like you've already thought a lot about it so it's kind of stupid for me to suggest to go back and have think again. But no one on here can know exactly what your feeling before sparring or during, or even right before you throw up...
You've suggested maybe it's nerves?
For that i'd suggest trying to relax as someone else suggested. But make a very concious effort of relaxing. Look on the net for some relaxation techniques you can use just before sparring to calm your nerves. Their is a lot of things you can do to relax your body and mind and really take the worrying sick feeling out of your head. Some times before I go in sparring I feel like I have to take a wizz. I always pee before I go to the gym so I know it's just nerves, but your body can react in some very strange ways according to whats going on in your brain. So my suggestion would be too look for some ways to really settle your mind down and that could really help. If you really want to get serious with that idea, do a search in limewire or bearshare for "hypnosis" or "self help" or "relaxation" and their will be tonnes of MP3's that you can listen to that'll help train your mind to relax and overcome any fear-blocks that build up in your mind about sparring (or anything else for that matter). An even FURTHER step would be a book called "Unlimited Power" by Anthony Robbins. A few techniques in that book can help your mind overcome antyhing.

On a physical level though, maybe you should spa in a different manner to which you are now. If you are going in with strangers and that makes you nervous a little,,, try convincing a friend to spa with you, or your trainier (if you trust them). It doesn't have to get serious or physical, it just has to get you feeling very comfortable with moving around the ring, having punches thrown at you, moving backwards and forwards and throwing your own punches. The punches don't even need to be hard, they just need to get your mind used to and comfortable with that environement/situation.

I don't know your story but if you're not that experienced and your trainer is sending you in the ring with experienced people who intend on knocking turds out of you for the whole session, then god you SHOULD be feeling sick. Their's been a few discussions on ways traininers use sparring in their training.. Some trainers just throw whoever in with whoever and let them go to town, and learn the hard whether they are good or not... I personally think that's a useless way or training people unless they BOTH are really wanting to go pro or take their game to the next big level!
Then theirs the trainers that see each sparring session as a time to work on your weaknesses and skills and NOT to just knock people out. This manner you can still put whoever in with whoever, but the intention is to LEARN and not HURT.
Unless your quite experienced and confident, it IS hard to spa with someone you don't know enough to trust and you do worry what could happen.. It's pure instinct to worry (until you feel confident/comfortable). So if this might be the case, FIND someone that you TRUST to spa with. And get comfortable with them until your confidence is up enough, until your ready to get in and start sparring with other people. You'll know when it's time because you'll WANT to get in and spa with a new person. It'll be exciting to you!
Just if you are throwing up and feeling sick every time you spa, it's obviously not very productive or enjoyable, so try something different and see if that helps??

I have no idea from a doctors perspective, but hopefully some of my advice can help you. I don't know many diseases or illnesses that ONLY come into effect and make you throw up if your a boxer and your heading into a sparring session.

Look after yourself, Good luck and hope you feel better!