I do all the time. In stores I'll sing and sometimes dance a bit too and only realize when people look at me funny. Lol.
Recently I had my headphones in and my whole family was staring at me. I asked them if my music was too loud and they told me no, I was singing. I dont even realize I'm doing it.
No embarrassment at all. For me it's a sign of being happy and we all need a little more happy I think.