Hello! Although you are right to suspect that it could be a sexually transmitted disease, be sure to consider that there are a multitude of other rashes and infections that you can get on the sensitive skin of the penis. For a definitive diagnosis you will have to have a swab and culture done at a doctors office to send to a lab so that they can figure out what microorganism is causing this.
What you may be describing could be primary syphillus. A single sore (called a chancre) appears about 10-20 days after exposure (but it can be more) and is usually firm, round (even edges) and painless (though if it is irritated, it can be painful). It will usually heal in 3-6 weeks without treatment, so most people don't follow up on it and this is where problems occur because the sore disappears but the disease progresses to secondary stage. If you suspect this is what you are experiencing, you definately need to see a doctor who will probably put you on penicillin.
If this is less of a "spot" and more of a spread rash that reaches around your penis, the itching and peeling sounds like what you may be experiencing is a yeast infection. Once confirmed that this is what it is, this is easily treated with over the counter medication and prevented by having your partner treated as well.
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