If you want to take him the doctors then do so. It's up to you and as him mum if you want him to see a doctor then he should.
Rashes can often be just rash and be no more than a rash so try not worry, especially if he seems ok.
Ellie often gets dry skin in the winter due to cold outside and furnace like conditions in our house.
So it's up to you, I'd you're the slightest but worried see a doctor.
When I had my first baby I was at the doctors every week to the point that I know the gp was pissed off with me lol. But now I wish I'd have told him what I thought of him, he should have been helpful! But hey I was very young