What can be causing this weird feeling when I press down or chew with a new crown?

Hi:It's best to go back to your dentist and check the bite and the crown to make sure all is ok.Best,Dr. Maddahi

Hello, my name is Miles.  I am a prosthodontist.
The issue you are describing may be one of two different things (or both). It may simply be that the crown is too high and requires only a simple in-office adjustment.  Alternatively, it may be that the tooth itself has a crack in it - in which case the tooth may need to be extracted if the crack runs deep into the root.  Clench your teeth together and release your bite.  Pay attention to the sensation.  If there is discomfort during the releasing portion of biting, it is often a good indication that there is a crack or fracture through the tooth/root.  I hope this helps!
-Miles

It sounds like your bite may be off. You need to get your dentist to reevaluate your bite as your tooth may be sensitive without the adjustment.