Heavens but this is absolutely typical behaviour! Do not feel badly of yourself.
If throwing tantrums had ever become an Olympic sport, ds1 would be been a triple gold medallist. I also have memories of carrying out of shops like a rolled up carpet.
Probably his worst tantrum occurred at the bus station when I had two bags of shopping, ds2 (aged 3 months) in a sling and ds1 on reins. The "wrong" bus (a single, rather than double-decker) had the temerity to arrive and on discovering that we would be catching it and not waiting another half an hour, ds1 rolled around on the very grubby ground shouting "No! No! No! Want Big Bus!!". He screeched, he rolled, he kicked, he gave the impression of a Baby Banshee. I picked him up by the back of the reins, carried us all onto the bus where he promptly carried on wailing like a pig being slaughtered.
An elderly lady looked at me as if I was the worst mother in the world and said "Poor little boy!". I am ashamed to admit that I suggested that if she was so entranced by him, she might care to have him bouncing and screeching on her lap. She suddenly lost interest...
What I would say is that shopping trips and children this age rarely mix well. If at all possible keep the shopping to a minimum and make sure your child isn't already over-tired or hungry. To be honest, I've often felt like throwing tantrums myself in shopping malls so it is no surprise that they so often bring old meltdowns in toddlers.