Are the gypsy moth caterpillars bad around you? We've had a huge problem with nasty bumps from the toxins in the little hairs on their legs (which also come off when the caterpillar is bothered or even sprayed, and then you can get a reaction just by sitting in the grass. Also the hairs can blow in the wind). They're hard or impossible to see. I find the bumps don't respond well to cortisone, unfortunately. This is the first year we've seen this, and we've been in our house over 20 years.
I also think they could be small spider bites - they tend to appear in clusters, and often where there is constriction such as a natural fold in the skin, under a waistband, maybe the diaper elastic, etc.
Flea bites are possible but I would think everyone would have them. Fleas jump, so bites on adults are usually from the knees down. On a baby they can be anywhere.