This sounds EXACTLY how I react to spider bites! I am allergic to their "saliva" & the "little white bumps" that you're describing sound like an allergic reaction. I actually went to an allergist & that is the info that they gave me. I definitely would contact your doctor just to be on the safe side, but he should be ok. I mean, mine are itchy & they hurt for a day or two, but it's not life threatening (at least for me, anyway).
One thing that I would look out for (and you may want to bring this up to your doctor & see what he says), but MRSA is going around & so if your son DOES start scratching them & they become open sores, he would be more susceptible to MRSA. MRSA is caused from skin to skin contact through open sores.
You can find out more about MRSA on the following website:
____@____.com/ncidod/dhqp/ar_mrsa_ca_public.html
Good luck to you & your family.