wow. i'm sorry!
I keep telling my husband that i wish my son could just outgrow everything and i'll take on the allergies -that's pretty much what you're living.
my allergist told me she once tested a new born baby but that was a very isolated incident and they don't normally do that. My son was tested at 7 months. So it really depends on the allergist.
You may need to go on an elimination diet until you find out what's causing it. Or even do formula if you can't figure it out. I would first go top 8 free and see if he's better. Or milk/soy free first. good luck!