What shoes are you wearing? This would be the first thing to suspect.
I've often noted my feet hurt after squatting. I attributed it to the flat soles of the lifting shoes, but paying more attention I noticed the soreness is coming from the outsides of my feet, probably from pushing. My stance is slightly wider than SS teaches, and slightly more open (it was moreso but I've tightened it up some). Like most lifting aches and pains they go away in short order, but I wonder if it is an indicator of an adjustment that should be made, either stance distance or foot angle.
What shoes are you wearing? This would be the first thing to suspect.
VS Athletics, the regular ones. My arches are fine, but the inside of the shoe is as flat as the part that goes on the floor, and I haven't put any sort of support in because I wanted to keep the foot/shoe/floor connection as direct as possible.
First thing to try is an arch support.