Oily skin is not related to diffuse thinning of hair. If you have hair loss or having oily skin/scalp issues see a doctor for an examination to find possible causes and treatment options.
If you put topical minoxidil on your head it should not grow facial hair. In rare cases some women report peach fuzz hairs growing on their face.
The cause of your hair loss is likely alopecia areata but you need to see a practitioner as there are other potentail more serious causes including infections which can lead to permanent hair loss if left untreated. If it is truly localized AA, I tell my patients 75% grow back in 12 months...