by the way Alcavis is basically bleach but safer and in much lower concentration.
It could be heat rash!? it's a pretty warm spot on the body. However I get red spots and a little swollen with a kind of white spot in the middle depending, that is usually caused by putting pressure on a certain area and that i was told is a circulation thing.I am not a proffessional so unfortunately that is the only idea I have for possible answers.
about cortisone again, there is actually something called "Tinea incognita" when fungal infection is treated with cortisone the infection is hidden to the sight but is still present and actually fostered by the immune suppressor. therefore the name "incognita" , hidden.
cortisone might work in reducing the redness but it won't remove what caused it. it should only be used as a last resort and only when necessary.
a dermatologist should be able to recognise what it is, although I wouldn't really bet on it... skin biopsy should be able to identify a possible infectious agent.
try a innocuous home remedy first, sponge his armpit with a low concentration of water and Sodium Hypochlorite. 0.5% should do.
I don't live in the States but I believe there are pre-made solutions on sale under the brand Alcavis. it should be enough to remove whatever common bacteria or mold.