This would be great to get looked at by a Dermatologist. We can get all the same skin things the rest of our body has on our penis. This sounds like in the psoriasis or eczema category from your description. A doctor would tell you what to use on it as some otc products could be irritating. Think you can get to a doctor? I do want to say though that friction can cause this as well if you've had any type of sex or masturbation recently that was a little more than the penis was ready for. If that's the case, lubricant is your answer.
Because it could be several things you need to see a doctor to get it diagnosed. Could be ringworm (jock itch), could be eczema, could be lots of things. There are lots of different treatments for different things, but you can't know what to do if you don't know what you have and you can't know without someone medically trained taking a look at it to see.