PA28R pilot reported increased pressure required on yoke when adjusting pitch.

Narrative

I was flying the ILS XX at ZZZ. Upon reaching the FAF; ATC directed me to switch to Tower frequency; but I couldn't make out what the controller said. When he repeated shortly thereafter; I switched to the Tower about 2 miles short of Runway XX. Shortly after I switched to the Tower; the controller asked me to execute a go-around. I put in full throttle and hit the go-around button which set the pitch for a climb. I cancelled the auto-pilot shortly thereafter but realized that my yoke required a lot of forward pressure to achieve level flight. I then realized that the pitch wheel was set for maximum pitch up. I tried to manually adjust the pitch wheel and it would only slightly move with significant force. I switched the autopilot on/off several times and the trim wheel adjusted slightly. At this point the trim wasn't significantly out of position; but I did have to maintain meaningful forward pressure on the yoke for the flight back to ZZZ1. I notified ATC of the concern; but as I slowed down on the approach into ZZZ1; the yoke didn't require much pressure and I was able to land almost as normal. Maintenance subsequently inspected the airplane and noted that the cable was bound up on the drum in the back of the airplane.