If you have a greaseable rudder port, grease it. Also, with the boat out of the water, grab the rudder and try and move it fore-aft and side to side. If it has a lot of play, that means the rudder port has been hogged out over the years, the rudder post is severely worn, or both.
If this is the case, the steering will work fine out of gear, but when running, the thrust from the prop push the rudder post cockeyed in the rudder port. This can cause hard steering or even cause the rudder to bind up like you have described.
Just to check the simple stuff before tearing out any underwater gear, I would also disconnect the steering cable from the tiller arm and turn the wheel in both directions to ensure there isn't any binding in the steering cable or the helm itself.
1992 Supra Mariah - Red
PCM 351HO 285hp - PCM 1.23:1 Transmission
OJ XMP 4 Blade CNC 13x15.5RH
"People do weird things to boats" -Unknown