the haircut situation is a tough one since you're pretty much stuck there until they're done with you. Personally, I always carry around my music and headphones so if there is a situation that is triggering I can tune out and listen to something more calming/upbeat/whatever you choose. Which works for normal shopping. (In fact sometimes I just plug in headphones before hand so I don't even have to worry about it haha). Another technique that might work for you is being on the phone. If I'm nervous I call up a family or friend (sometimes multiple) and even if they don't answer I leave them funny voicemail and tell them about my day and that works too.

Unfortunately neither work for the hair thing :/ I guess my only solution idea for that is trying to engage with your hair person and talk to them/try to get them to tell you funny stories about other customers and see if that helps take your mind off it! (This is also why I go to a Korean place to get my hair done since they usually are playing music in their language and so I can't understand it at all hahah).