@Downonthefarrrm you're not the worst at all! If you were DC would be smashing up the house, smacking kids and head butting a wall while you had a good laugh. But you're posting on here for advice, that takes balls.
I know the perfect people who like to stare at you when you're out, if your child dares so much as fucking whimper. Just apologise to them, explain not everyone was perfect like you dear. Then carry on. Or give them the finger, both work equally well.
I remember getting death stares in McDonald's of all places because DS kept dropping book on floor and getting me to pick up, was a game for him, he'd pretend cry until I passed it back. I just looked at her and said if you want a quiet coffee then fuck of to costas.
I will say DS is suspected ASD but I'm not suggesting your child is.
If there's a tantrum in the shop I try distracting, as soon as we enter 'look at the list, the first thing we need is milk, let's find the milk, where is it? That's not milk it's juice! You like juice don't you?' Constant, all the way through. Same with bus journeys, walks, everything. I find if I talk about what I'm doing, what's around us etc he concentrates more on that and it's working well so far. I take toys and books too.
You'll find it gets easier, you learn how to respond, what works best and it gets better once they learn to communicate.
I bet you're doing a great job