Most likely it's eczema, a very common rash on the penis (and elsewhere.) It's aggravated by friction but not caused by it. It's usually hereditary, but is most certainly not sexually-transmitted, in you or anyone else.
I'd treat it by applying over-the-counter hydrocortisone twice daily when it's active and stopping when it's no longer bothersome. The condition comes and goes. Don't rub or pick at it if you can help it.
A visit to a skin doctor for confirmation of the diagnosis and treatment suggestions would be a good idea.
Best.
Dr. Rockoff