I Have Been Having An Issue With My One Hand.

I have been having an issue with my one hand. I've had raw, dry, flaky, peeling, and itchy skin on two and a half fingers. It's been ongoing for a few months. I've tried multiple lotions and creams. Some make it burn. I've put lotion on it with a glove over it while I sleep. Nothing is helping. I've also started breaking out on my chest. I took Tylenol cold and sinus over a week ago. I noticed I started breaking out. Last Tuesday was the last dose I took and I'm still broken out. Should I make an appointment with my doctor or my dermatologist?