Ok, unfortunately, there is no great "cure" for heat rash, which is what it sounds as if you have. You can try these things to attempt to treat the rash. You can using a hydrocortizone cream in the area to reduce swelling and itching, or cover the area with calamine lotion. You can try applying "dusting powder" to the area. You can make this on your own following this "recipe":

DUSTING POWDER

Formula

2 cups arrowroot or cornstarch
1/2 cup baking soda
1/2 - 1 teaspoon fragrance

Instructions

In a glass bowl, mix the ingredients well. Pass through a sieve to remove lumps. Store in a used talcum powder dispenser or salt shaker.

You can also try sitting with a fan directed at your armpits after showering and before dressing. You can try using a diaper rash cream on the area. I would recommend Desatin, J & J, or Super Duper Diaper Doo. They work the best in my opinion. You may want to try taking oatmeal baths to reduce the itching and pain. Try looking here for more tips on heat rash:

http://www.associatedcontent.com/article/313905/how_to_help_relieve_heat_rash.html

If you try multiple things and the rash still seems to persist, you may want to visit a dermatologist to determine whether it's more severe, but from what you are describing, it sounds as though you are accurate in describing a heat rash. I wondered for a short time whether it could be a folliculitis, since most women shave their underarms, but since reducing the shaving didn't seem to help with the rash, I would probably not pinpoint that as the reason at this point. I hope these remedies help you to get some relief.