I've had some hooks over the top of my doors for the past few months. I think either the doorframes have warped or the doors themselves have started to droop under the additional weight, as they now stick when closing.

I've tried tightening the screws that the doors are hanging on, but it's made no difference.

I'm considering two options:
1) I'm aware I could plane away an inner part of the frame and repaint, but I live in a rental flat, so I don't want to do any major carpentry that I might botch.
2) I could take the doors off entirely and rehang them using longer screws, and futz about with it until it fits nicely in the frame again.

Is there a more straight forward fix that I'm missing?