This sounds like dry skin or eczema, not an STD. Bactroban wouldn't help much, because that's for bacteria. I would try hydrocortisone 1% and lubrication. Avoid rubbing, but you say it doesn't itch.
If you can't clear it up in 3-5 days, or if it recurs, you should see a doctor for proper diagnosis.
Take care.
Dr. Rockoff