nah you aren't alone, it's the age.
This is my second 'bolter' and I've learned better than to let him walk on his own at the shops. My DD was the same. He is either in the stroller (I know it's a pain for quick trips but it's contained and I'm not struggling with a wriggling kid while I'm trying to do other things) or in a trolley. He doesn't sit in the seat well so usually doing the groceries I have both kids and all the groceries.....we get lots of stuff squashed but hey
Also in my bag are; a couple of small toys each, a notebook and pen/cil each (really bad when only one gets one), a mini magnadoodle and a bottle of bubbles...if nothing else I entertain the other shoppers while they're doing they're shopping.
I'm prone to opening food that I'm buying while we're shopping so they have something to eat. I also often sing....I know - who the heck is that crazy lady.
I have learned that letting it get to me solves nothing at all, only makes me angry and really doesn't resolve the issue. I deal with the issue once with a 'not today babe' and that's it we keep walking. When it's getting really bad I make an effort to use an upbeat singsongy type voice to keep everything light. I rarely offer rewards or bribes cos that backfires sooner or later (I learned with DD).
Little people are just like animals (no horrible connection here I promise) - they can read us better than we can read them and they feed off our energy.

Oh and think nothing of the people that stare - they have nothing better to look at - what they think of you means nothing in your life so please hun don't let that be an added stress.

I really do know how hard it is.