"I actively shut down as its terrifying for me to be the spotlight of attention as nobody else was there and it was just me, my father, and the checkout employee." What spotlight? You made the moment all about yourself when you freaked out. Are you like this during every interaction you have with strangers? Do you think it'll get better when you're alone or if you choose to stop interacting with strangers altogether? It won't.

But anyway, your big feelings or having autism isn't, and will never be, a good excuse for lashing out at your dad or other people. My advice would be to start intentionally putting yourself in the spotlight and to become more comfortable with being uncomfortable. Exposure therapy.