Face rash on chin

For the last six month, I have a rash on my chin that I can't get rid of.  I'll wake up in the morning and it is white, looking like dry skin flakes.  I've been putting a cream on it (anti-fungal) but it doesn't seem to help.  When you touch the skin, it is rough.  Some days it isn't noticeable at all, other days it is quite noticeable.  I cannot figure out a pattern to it at all.  I've been going to a dermatologist for the last few months and nothing has helped.  It doesn't seem to spread, or be contagious.