Bad Crown Fitting. What Are My Options From Here?

The best thing to do here is talk to your dentist about it. Communication is the most important. Let him know that you are not satisfied with the final result and find out what he will do about it. Sensitivity may settle down but there are clearly more concerns here.

Photos would have helped here to answer this adequately. Your bite may need further adjustment to relieve sensitivity. But if your crown has already been over-adjusted and has `hole' in it, new crown with better fit will be the best choice. I suggest you talk to your dentist or get second opinion. 

Sounds to me like you should replace your dentist before you replace the crown. A well-trained and experienced cosmetic dentist would never put something like that permanently into your mouth. Of course, I do not know all the circumstances! Were you more concerned with cost than quality?

Hard to tell from what you have written but I would talk to your dentist and let them know your concerns.  The sensitivity could be from the bite still being off and a simple adjustment may fix that issue.  In terms of how it looks, you would need to have the crown replaced.

Before any crown is finally cemented should be tried on. As well as shape, color and occlusion should be checked. In some offices the crowns are literally pushed for cementation. I think you should ask your dentist to redo the crown. The good crown should look real and natural as a real tooth.