Your description doesn't remind me of much of anything. It isn't
molluscumMolluscum contagiosum
Molluscum contagiosum - close-up
Molluscum contagiosum - close-up of the chest
Molluscum contagiosum on the face, because those don't "clear almost completely" and then come back. You may be on to something when you say, "Although I do see him playing with them once in a while." Kids do that pretty often, which can produce bumps and redness. I doubt there is actual "pus," which would be white.
I assume each doctor you consulted saw only mild irritation, and so prescribed cortisone. This is not unreasonable.
My advice is to use the cortiosne from time to time to quiet things down, not to worry too much about cause, and to wait from your child to grow out of this, which I think he will.
If the rash stops responding or worsens, show a doctor again.
best.
Dr. Rockoff