wobbeling rudder post
I have never had to deal with this personally, but my understanding is that you will need to drop your rudder to see exactly what the problem is. The two most likely are worn out bearings or a badly corroded post. The post is of course a potentially dangerous situation. I have also read that those bearings are very expensive. But you could contact a boat yard and describe the problem to them.
Good luck, I hope others will have more precise advice.