Hi @Number2, I buzz cut my hair when it started falling out, it was more comfortable once I did that, but I left the rest to fall out by itself. I think I read somewhere that it was better to leave a bit of length to help the hair fall out.
Biotene mouthwash helped me a lot, I had a dry mouth, especially at night, and I'm sure I read on here you can get an oil you can use for your nose.
I would talk to your oncologist or breast care nurse if you are concerned about the lumps under your arm, they will know if it's a known side effect, or something they want to check.