Will medicare pay for a broken nose that's causing these problems?

Hi and thanks for posting this question!
You will have to verify this generalization with your individual insurance carrier:
Nasal surgery addressing the septum for reasons of breathing difficulty or to repair traumatic injury is generally covered by insurance companies.
Nasal surgery to improve the appearance of the nose is considered cosmetic and is an out-of-pocket cost to the patient.
The best way to find out if you meet the criteria for insurance coverage is to be seen and evaluated by a reputable, board certified specialist in nasal surgery (either plastic surgeon or ENT surgeon).

Best wishes

You can expect insurance to pay for functional problems like septal deviation and difficulty breathing.     It will not pay for the cosmetic part, changing the appearance of your nose.    Go see a good nasal surgeon and find out what will be covered and what will not.