Classical music is so fabulous

whenever I put on dramaticmusic without lyrics I always feel like I'm in a movie haha. Earplugs is a great idea

if you're worried about other people's opinions, you may want to choose ones that don't show as well or cover them with your hair or even get ones skin colored so that they "blend" in. My mom gets lazy and just smushes a bit of kleenex in her ears so you could consider that too!
I would definitely suggest checking out the place first since it really depends on what kind of crowd they cater towards. I've actually recently been getting my hair done by a lady who owns a little booth in a giant group of hairdressers. She has her own radio too so I could totally request a station or bring my own CD/usb/whatever works. If you can find an individual hair person that would definitely work too
I hope it gets easier for you