What are your symtoms? and any thyroid blood testing done?
http://www.medicinenet.com/rosacea/page2.htm
"Rosacea strikes both sexes and potentially all ages. It tends to be more frequent in women but more severe in men. It is very uncommon in children, and it is very infrequently seen in darker skin tones or black skin."
Some people with hypothyroidism have rosacea and there could be a connection, but, it's not a direct symptom.
Why will your doctor not diagnose your thyroid condition? Have you had blood tests that confirm hypothyroidism? If so, please post them, along with results, and be sure to include reference ranges, which vary lab to lab, so must come from your own report.
Do you have other symptoms of hypothyroidism? If so, which ones?