If a crown is not adjusted right, lots of problems can develop within a short period of time. Make sure he or she does the adjustment right because it can cause problems if not adjusted right.
A dentist did two crowns at the same time on my teeth and he left them in hyper occlusion.
I don't know if this is what your dentist did or not, it doesn't sound like it but.......
I do know if you have any discomfort more than a week you better get back to a dentist and get what ever is causing the problem fixed; even if it means sending the crown back to the lab if she or he cannot get it adjusted right.
occlusion is everything in a crowned tooth, I have been through pain for almost a year with two teeth crowned from a dentist.
All crowns should be flossable on both sides, no matter what. Labs consistantly make crowns just slightly too tight to offset the errors from an indirect method and because the dentist is supposed to smooth the crown down until you get a perfect fit.
The feeling may go away, but it will take time. The crown was probably made correctly, but it sounds like the dentist did not spend enough time adjusting it.
Whenever you get a new crown, floss should snap through, which shows a contact that is not too tight or too open.