OP. Where do I start? I despair of the support that is not given to, and the ignorance surrounding, allergies in this country. I suppose its better than it used to be, but there's a long way to go. Unfortunately you are going to need to fight your corner on this one for a referral from your GP I'm afraid, and go to a different GP if needed.
My DD had a very similar contact reaction to CMP (cows milk protein) when she was weaned at 6 months (EBF so no milk until then, although bad eczema due to CMP and egg in my diet). She never ate any CMP (well, a tiny crumb of cheese), and we never, therefore, had any internal symptoms. She is potentially anaphylactic to CMP and eggs.
At no point did any HCP suggest I should feed her any CMP to 'see what happened'
. The correct procedure is a referral to an allergy consultant at your local hospital, who will take a case history and most probably do either skin prick tests or RAST (blood) tests to try to establish the likelihood (there is no conclusive test) of her being allergic to the most common allergens (dairy, egg, soya, various nuts etc). This will help you to know what is safe and what is not safe to wean her on to at home, and what you need to avoid until she is older and (hopefully) grows out of it. After a reaction like you describe, you should absolutely and utterly not try it at home, no matter how small the amount.
Sorry to be so draconian/forceful, but it may be potentially life threatening. It may not, hopefully, but there is no way to test that in a safe situation unless under specialist consultant care.
It may help to ask MNHQ to get this post moved to allergies, where lots of others besides me can help, advise and support. The support and knowledge there is incredible, and lots of them will have been where you are now. If you 'report' one of your posts, and ask for it to be moved, it should be easy for them to do.