First and foremost if they are potentially staph infections, then you need to treat them properly. They must be thoroughly washed with soap and water, bactricin/neosporin (max strength since your dr. didn't provide you with prescription bactroban), then covered with band-aids, preferably those water-proof types like those made by Nexcare. If the area around these bumps are hot to the touch and swollen, they probably are filled with pus/infection. Warm compresses or heat pads should be applied.
My son's dr. drained his when he got three while on vacation (they all started with one mosquito bite on his arm, then spread to two places on his leg that had no injury what-so-ever.) Draining is gross, smelly and painful, but it's worth it, since they won't heal until the little white "plug" part comes out. They can leave pretty bad scars as well, since the infection can get deep. My son was also on a round of cephalexin. He hasn't gotten any since, but he has three dark scars from them. I am also prone to staph, so whenever I get even a razor scrape, I wash, spread the neosporin, and cover it. Thank goodness they make those tiny little circle band-aids now...we go through quite a bit.
I'd definitely take him to a specialist. It seems like most general practicioners do nothing these days... no cultures, no testing, nothing.
BUT-if it's not staph, then it could be dust mites or bed bugs. Some people are allergic to dust mites in ways other than sneezing. I would try zipping up his mattress in an allergen cover, get new pillows, and put the allergen covers on those as well. Then buy yourself dust mite/allergen relief laundry additives and wash all his pillowcases, sheets, blankets, etc. I've gotten some from this website before: www.natlallergy.com/