I can see why you would post this question here, it's a difficult situation that you obviously have some major concerns over. First of all, I THINK, that she should see a doc, the same as everyone else suggested.
Now here is the part that you might not want to hear. When a girl or woman has a huge secret she's been maintaining for a very long time, acting is one thing they are able to hone as long as the one thing they "think" they need isn't threatened by being discovered. In other words if she has been telling you for a long time that her tongue swells up and she has this major reaction you should stop and ask yourself if you've every actually seen this happen. If you've never had a first hand experience of the swelling and reaction then you should take her to a doctor to make sure you don't jump to any conclusions.
Now here comes the sticky part, if she's hiding bulimia and she knows that you are sympathetic to the fact that she has an alergic reaction every time she eats meat then that might be her "out."
It's a difficult head battle when it comes to eating disorders and the only thing I can provide is first hand experience with the disorer itself, but I am not a doctor. Get her checked out and if it's not an allergy, then the best thing is to discuss the possibilty of an eating disorder with your doc, and see what he/she says.
I wish I could help more, I hope all works out well.