As an adult, the only risks for HIV are:
1) having unprotected, penetrative vaginal or anal sex, or
2) sharing IV drug needles with other IV drug users.
If all of your encounters were protected, you have no risk for HIV. Please note that you may still be at risk for other STDs and herpes, but not HIV.
There's nothing more that can be said. You had no risk for HIV. Ergo, your rash is obviously not related. Go see a dermatologist. Quit using scented soap and detergent. This has nothing to do with HIV because you had protected sex, which is NOT a risk for HIV.
You're not at risk for HIV. Keep using condoms and you won't have to worry.
Your rash is probably from the gym. Probably a sweat rash.