Hopefully this is better. If you have an allergic reaction on your skin, especially on a sensitive area, it may take some time for it to be normal feeling again. The issue is mostly cleared up and you are getting better. I'd give it a bit more time and see how you are in a week or so. If it is still sensitive, I'd go back to your doctor. But likely, this is a time related situation.
First of all, you can't get an STD by someone just touching your penis. The doc is probably just guessing, but he is referring to the oil used. It might have contained something your skin is sensitive to. Unless you had unprotected sex with someone else, there was nothing in what you're describing that involves STDs. It's probably just your anxiety about STDs that's causing this. I'd suggest you do some homework about how to get and how to prevent STDs. If you have a lot of anxiety about it, only have sex with someone you know, as those who are paid to have sex just really can't always be careful if they want to make a living. A lot of topical products people use, especially from drug stores, have things in them one really shouldn't put on one's skin, and if something happened that's most likely it. But the rest is probably your anxiety.