Can I take 15mg of Biotin per day?

Taking supplements at high doses may be harmful to your health. It also will not likely treat any hair loss issues. See a doctor if you have concerns.

Because it's so rare to be biotin deficient, there is no recommended daily allowance or RDA. 15 mg dose is extremely high. I would advise to check with your physician before commencing. if you are truly deficient in biotin, supplementing could be a good idea. 

Biotin deficienc is typically seen in the pediatric population
and the association with adult (female or male) hair loss is WEAK. Biotin deficiency can cause
hair loss as one of its symptoms (along with seborrheic dermatitis, dry skin,
brittle nails, fatigue, intestinal tract issues, muscle pains, and nervous
system problems). Even a cursory
search of the available medical literature will demonstrate that Biotin deficiency is also RARE among
the adult population.Therefore, widespread supplementation with Biotin is likely unnecessary
and unlikely to improve hair growth. An exception to this would be those patients consuming large amounts of
egg whites (i.e. more than 20 raw egg whites per day over a period of weeks to
months) or with absorption problems (i.e. on parenteral nutrition etc.), and
excessive/prolonged antibiotics and anti-seizure medications.Fear not though, Biotin (AKA Vitamin H
and B7) is water soluble, so taking excess Biotin from a costly supplement only
results in expensive urine...GOOD LUCK!

I went to Wikipedia to look up your question and through you should read about Biotin in the web reference below.