It sounds like Lyme to me.
You can view some typical Lyme rashes here:
http://www.lyme.org/gallery/rashes.html
I would strongly urge you to see a Lyme experienced physician, which you can find by typing in your location to "Flash Discussions", then "Find a Physician" here:
http://lymenet.org/
Be aware that testing through the commercial labs is notoriously insensitive, with the FDA-approved test kits missing over 50% of positive cases.
In my opinion, IGenex, which specializes in tick-borne diseases, is the only reliable Lyme lab, because they test for multiple Lyme strains, not just the B31 Shelter Island strain, and they report on the most specific Lyme markers, the 31kDa and 34kDA bands. IGenex has recently passed Cal., NY, and CDC quality testing with flying colors. You can download the IGenex testing forms from my website; give these to your MD if you want to use this lab. MDL isn't bad a bad lab either.
Fewer than half the people with Lyme ever see a tick bite or a rash. Early treatment is essential with Lyme, so don't delay.
KrisKraft
http://www.lymediseasefilm.com/
The first thing that comes to mind is Lyme disease. Although this is usually from the bite of a deer tick, there have been a couple of cases reported to have been spread via mosquitoes. Another bulls eye sort of bite is ring worm which spreads via the touch. If you touch one bite, or scratch it, and then touch another area of the body, you have it there, too. Ring worm can be quite nasty if left untreated. This can be contracted via cats, birds, or other carriers who "leave" the virus behind to be "picked up" at the next touch. The black widow spider bite also has a red dot surrounded by a ring. If the child found a newly hatched egg (can be hundreds of tiny spiders) this could be his problem. The last idea is scabies. This is caused by a parasite under the skin that travels throughout the body leaving little itchy red to purple bumps with an outter ring of red. Either way, you should take your child to a dermatologist. They are "up to date" on these sorts of things and should be able to identify the rash. good luck