That's not how HIV is transmitted. You can't get HIV from a cut on your scrotum, no matter what. HIV enters through your urethra, and would NEVER enter your body through superficial cuts or scrapes. If you had a cut big enough to allow HIV to enter your bloodstream, you would be at the hospital - not having sex.
You were never exposed to HIV and you didn't need a test at all. See a doctor about the rash on your back. It has nothing to do with HIV.
RNA PCR is not intended as a primary diagnostic test.
What was your risk event?