Hi OP
Whether or not he is abusive, I am nowhere near enough of an expert to say, but he was certainly a dick in this episode.
I do have to walk on egg shells somewhat with him and I was feeling quite anxious in the shop as I had a feeling that he would be pissed off if I took too long
This is not how you should be living, not a few weeks after having a baby, not ever. You should not be living in fear of your partner. I have been the child in this scenario, where multiple scenes were caused, unreasonable punishments were given to me and my mum for disregarding some bizarre rule that no one knew about in the first place, etc etc, and it can fuck you up for life. If it's causing problems now, it may not get worse, but it is unlikely to get better if you just sweep it under the carpet because you "undermined" him and thus his actions are explicable.
Like I said, I have no comment on whether or not he is abusive, but it needs addressing, especially if it's not the first time. I don't think it can be written off with "well you did undermine him, what did you expect? People get angry and aggressive when you do that". If it's a one off at a pinch-point of stress and you can both apologise and move on, then it's not the end of the world, it's normal. If you have an ominous feeling that you are going to cause upset just by spending a few minutes in a supermarket, or because you buy something you can afford that he won't approve of, that's a pretty shit way to live.