What could be causing my garbage disposal to be so noisy after unjamming it?
There is likely a small bit of hard debris jammed between the rotating shredder plate and the wall of the disposer. By design this is the area where food particles get ground up. By your description it sounds as though a hard bit (bone, metal, etc.) initially jammed the disposer shredder plate. You have now managed to free it up but a small piece is still stuck in there. I would continue to use it as normal and chances are the debris will eventually get worn down and get dislodged.

Modern disposers are generally not economically user-serviceable, but you could take it apart if you feel ambitious. Alternatively you could replace the disposer, but you might as well wait till it dies.