How long would teeth be sensitive after cavity is filled?

Varies: No set time frame. Could be a few hours to a few months. At the point where the pain does not go away or becomes unbearable, there's a good chance you will need root canal therapy.

Call your dentist: This varies based upon the condition of the nerve and the tooth, the treatment rendered, and your pain threshold. I would ask the dentist who filled the cavity, as he\she knows best the answers to all these questions and what you should expect.