TBDE, I would say to take them off BEFORE your feet explode if you can. The idea is to get to flare state less often, so if you can wear your socks for a while and remove them before the bad burn starts, you've kind of headed it off at the pass, as it were
Your foot is busy overreacting to every kind of stimulus with terrible pain and burning. You need to try to reduce the frequency of that if you can. Anything that helps, including short rests, is a Good Plan. Just no ice or cold surfaces. Elevation is good to head the burn off sometimes too...
Take care of yourself. I know how miserable it is when feet just go mad with this thing. It's horrible....especially if you're out with folks and there's no way you can NOT rip your shoe and sock off....yikes.
Bram.