My DS had a diagnosed case of CMPA that he outgrew when he was 2yo. He was diagnosed at 6mths old via a RAST blood test, and this was only after I had to push, push, push to get a referral to a paed (saw my CHN, 3 GP's in the first 6mths of his life and was told it was "just" colic). His symptoms were severe eczema (that was being separately treated), reflux (not too severe, not on meds), colic and wind pain and explosive nappies. He put on loads of weight though which was why his symptoms weren't all linked together by the GPs/CHN.
The RAST confirmed egg, soy, cows milk, nuts.
DS was exclusively b/fed until the diagnosis and at that point I decided it was time to take the paed's advice and wean on to prescription formula. I can't even describe the transformation - my DS rolled over for the 1st time, sat up for the 1st time, the ezcema cleared up, the reflux cleared up, he started sleeping through the night! The colic disappeared, he was no longer in pain.
He still has the egg and nut allergies and we are still under a paed, he is due to go back and see him in 6mths time for another RAST but I suspect it will be an ongoing thing (epipens watching everything he eats).
The things my paed did initially to find out what was wrong was several blood tests (RAST as well as some other ones I can't remember) and a stool sample for lactose intolerance testing.
I did an elimination diet with DD just to be safe, I b/fed her for a lot longer than DS, but luckily she doesn't have any allergies. I found the elimination diet very hard on a long term basis and did slip up a few times, which if she really did have allergies would have been a bad thing but obviously she could tolerate my slip ups. If you are truly going for elimination, I hate to say it but soy milk is a no-no, it has a very similar protein to cows milk and can cause all the same problems. I used rice milk.