The problem was being only able to run. I could only run and not walk. So when the bug started I wasn't overencumbered, but as I was stuck running I became over encumbered several auto saves later(I wasn't eating or drinking so my carry capacity dropped till I was.
I just tried it now and dumped everything and now I can walk again by pressing shift.
If I can help you understand the order of events: in the 1st caves, dropped off a ledge while moving against a wall, then I was stuck walking(I'm almost positive I wasn't overencumbered here). I tried switching some key binds and then at some point my situation reversed and I was only running and couldn't walk. I tried binding a key to the slow walk and then I was stuck with the slow walk. I restarted the game and went back to only being able to run. From there to now I became Overencumbered and was still stuck running, shift to walk didn't work and I imagine I should've only been able to walk(I think that's how it's intended to work at least when you carry too much). I dumped my inventory to below my max weight and things worked as normal.