All dental work is traumatic to your teeth. Most of the time they heal just fine, but eventually the nerve becomes so irritated that it starts to die. This is probably happening to your tooth.
Crowns require a great portion of tooth to be removed and this is a severe trauma to the tooth. If it was already sensitive, then this could have been the "straw that broke the camel's back."
i had a tooth become sensitive after a crown, and it stayed that way for about 2 years. Then it suddenly flared up and caused me horrible pain until I had the root canal. My advice is to maybe wait a little while longer, but if it doesn't get better pretty soon then go have the rc. You don't want it to go bad on you when you least expect it. Not fun.