What could be the possible causes of my crown hurting if had root canal there?

Crown has to be out. Any cavity or infection must be expose to air and drained, fast. A close space will lead to major problem. If a fully proper root canal problem was performed, there shouldn't be pain or discomfort, except for few days after the work. Again, get ye back to the dentist.
Good question.. There may be some inflammation or infection that has not completely resolved. The bite on the crown may be too high or may interfere with grinding motions if it is not properly adjusted. Please see the dentist who performed the root canal to properly follow up with your care. That dentist may know of particular reasons that are specific to this tooth.
Root canal failure. The root canal may need to be treated again. Bacteria can return and the original root canal can fail.