The Dental Crowns I had placed after 2 root canals seem to move slightly more than my other teeth. Is this normal?

If you feel that your crowned teeth are moving more than your other teeth and its happening after few weeks of treatment, the chances are that they are interfering in your jaw movements. Just see your dentist who could check and adjust them.

It is unlikely that your crowns will fall off.  If they are, indeed, moving more than before it is possible the bite is a bit off and should be adjusted.  It is also possible that you are noticing normal movement for the first time.  If you are concerned go back to your dentist and let them evaluate the movement.  I suspect you will find everything is normal.  Good luck!