Got a boil and it left a hole. How long will it take to close? Dr gave me antibiotics and said it was healing but it's been 3 weeks already.

Boil. It depends on how your skin heals. Sometimes it heals without problems, other times it may heal with a small scar. Time to healing may also vary. Give it another week or two and if no improvement have your doctor take so look again.
Maybe MRSA. Usually 3 weeks would be enough time. If it has not gotten smaller, or less red, then the infection may not be responding to the antibiotic. MRSA (Methicillin Resistant Staph Aureus) may not be killed off by just Bactrim (sulfamethoxazole and trimethoprim). You may need a different or additional antibiotic (like Doxycycline). Go back to MD if size is unchanged.