Hey Ladd. Sound like you got the elbow cancer.
Let's discuss...
No, this isn't normal and usually indicates an issue with bar position, grip position, a misunderstanding of how much the shoulder should be extended, a soft thoracic spine, or the bar moving around while squatting. The issue is technique that's been exposed by the increase in weight. It's not something you should "live with" and needs to be addressed since it doesn't tend to get better on its own.
The bar looks too low on your back in these pictures. Does the bar feel like it's sliding down lower while you're squatting? Does your bar have a center knurl to help it stay in place on your back? Can you take a video of your squat using the criteria in the sticky at the top and post it? We need to see you moving. Based on the moving elbows you talk about, it's likely the bar is too low and this is they body figuring out how to not let it slide down. Which will piss off the elbows.
In the meantime, can you set up the programming so you're benching and pressing before squatting, so it has less of an effect on those lifts?