How Long Does It Take to Hear Back from a Surgeon After Writing to an Insurance Company About a Procedure?

You would have to do a lot more trauma to your nose to cause trouble, especially since you are 6 weeks out from surgery. I'm sure your brain must feel a bit rattled, but your nose should still be in one piece. Repeating the trip, presumably for your next appointment, also should not be worrisome...

I can't think of contraindication to minoxidil after rhinoplasty. Nevertheless this should be approved by your own surgeon.

Yes limiting cosmetic surgery on the nose to just the "sides of nostrils" is sometimes a very reasonable choice but your main concern is a bulbous tip.  That would not be helped with such limited surgery.  You need to begin with a personal consultation with an experienced surgeon to...