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Janine, I don't think that's frivolous at all. You need and deserve those little things that make you feel normal and happy again. You've earned it!
Unfortunately, I don't have an answer to your question. I've never had manicures and don't know what to say. Of course you want to be careful until your immune system is fully up to speed after your treatment. I was told it takes about a year for that to happen, but I don't know if all doctors agree.
The only experience I can share is that my surgeon gave me a stern lecture on all the things I couldn't do for the rest of my life because I might get lymphedema. But heck, I do anything I want now. I shovel snow and cut grass and work hard in the garden with my hands in the dirt all day.
I don't know if there's any way you can check the salon's background to see if they have a history of safe work or if they have had cases of infections. (???) Taking your own tools sounds like a good idea if you have them, and at a minimum, ask anyone who works on you to sterilize their hands and work area carefully before starting to do your manicure.
I do hope you get the go-ahead for your mani/pedi!