should i feel embarrassed doing grocery shopping by myself, for myself

don’t overthink it. Everyone needs to have food to eat and if you are single that means you need to do the shopping. If you are embarrassed about that it just means you care too much what others might or might not think.

thanks to all who answered, you helped.

Not even a little bit.
Also, no one knows you are all alone when you go out in public.
They don't know you at all.
Every single person who has never found a partner understands this.

I'm sure there are plenty of people who do the same. It's really nothing to feel bad about. I have a partner but sometimes I shop alone and I find it hard because I have anxiety. So I can understand a little.

I find shopping for groceries a relaxing experience and have never felt it was an embarrassment. But if you feel embarrassed, just shop for groceries online and pick them up at the drive through. Task done.