I am not sure exactly what is going on without a bit more description of what the skin looks like but I can think of at least three possibilities.
The first is that you simply have some skin irritation from sweating and moisture. This is a common problem in the hot and humid summer months. The skin may look red or have a chafed feeling to it. This can often be fixed by wearing light weight wicking clothing, by using good skin hygiene, and by applying a skin moisturizer to protect the skin as able.
Another possibility would be that you are having some sort of sensitivity or allergic reaction to a deodorant or other cosmetic or laundry product that you are using. It is worth thinking back to whether, in the last month or so, you changed deodorants, detergent, or any other product. If so, it is quite likely that this is the offending agent, and you should try stopping it to see if the symptoms improve.
A final possibility that I can think of is some skin infection. For example, yeast infections of the armpits can occur, especially in humid weather.
Start by seeing your primary care doctor
again; he or she will take a look and try to figure this out for you.