I read the first few posts of this thread thinking why on earth would you be embarrassed by that. Then I came to the post about wearing something new and suddenly I wasn't so smug anymore.
Last year I needed new boots but it was when we were in lockdown so I ordered online. When they arrived they had a slight heel (only about an inch and a half). I'm quite short (5ft 3) but I usually only wear flats. When schools reopened and I wore those boots doing the school run I felt so embarrassed thinking everyone was going 'oh look at WitchS trying to be tall' 
I'm totally with you on all the hairdresser ones. God I hate everything about the hairdressers as it's so embarrassing.
Also going to the opticians when they put their face really close to yours with the little light. Excruciating. Then choosing new glasses is a minefield, how many pairs can I try on before they think I'm vain, what if they think my final choice is a stupid shape for my face. Then, after all that trauma, I have to actually wear the new glasses in public and everyone knows I have something new! Ffs!
A recent one is masks, especially during those few months when they weren't a legal requirement. I was embarrassed to wear one in case non-wearers thought I was neurotic, but embarrassed not to wear one in case mask users thought I was a covid denier. And don't get me started on all the other mask issues. I'd get embarrassed about my glasses steaming up, embarrassed taking extra seconds to pay with my phone because I have to input the code rather than it recognising my face, embarrassed taking my mask off when getting outside because people will judge where I put it (pocket- they'll think I'm disgusting; little sandwich bag then in my main bag- they'll think I'm neurotic). I'll be relieved when masks are gone forever just to be free of all the above scenarios!