is there another doctor at your practise that you could go to??
I had this, only with me rather than any of my kiddies, and altho my doctor agreed to test me (and confirmed), he then wouldn;t refer me to an immunoligist, which is the next person along as a reaction like this involves the immune system.
it took another very bad reaction from me, and another docotr at the practise, to get the referral that I need! (and I am now heading towards an epipen!!!!!).
if all else fails, yes you can go privately altho I am not sure how, or how it works. there will most likely be someone about here who knows that side of things.