Weird problem with first person camera in Skyrim

I had the exact same problem. To add onto what akselmo said, it is indeed Immersive First Person View which causes the trouble. The problem is that you failed one simple but crucial step before uninstalling - making sure you were not in first person view. The fix is simple: load up the save with IFPV then switch to third person view and save and quit, then remove IFPV. That's it. It even says to do this on the nexus page, something which I also initially missed.

Lesson learned: read a mod's uninstall guide before uninstalling because weird things could arise.

Quoting from the Nexus Page:

After uninstalling things are bad overall with first person view (camera in clouds, camera on horse feet, bow aiming goes extra far, camera is bouncing around, ...)

Make sure the DLL file from Data/SKSE/Plugins/FirstPersonPlugin.dll got removed properly. Make sure you are not using Joy of perspective skeleton. Make sure you were not in my mod's first person view on that save game when you uninstalled.

So you might want to check for that .dll file