Rubbing is not risk for HIV...Period
The irritated skin your worried about makes no difference, if these are your only concerns it is safe to move on.
To avoid infection,
You need to be using condoms for all anal and vaginal intercourse until you are in a trusting monogamous relationship and both have been tested for all STIs and HIV.
Everyone who is sexually active should have an annual exam and test for all STIs and HIV ,and always after unprotected intercourse. Always using condoms will give you peace of mind your tests will return with a negative result.