Pain Under Crown Months After Root Canal?

You would need a 3D Cone Beam Scan to determine if there is another canal that might have been missed during the root canal treatment or there is a root fracture. Regular x-rays is two dimensional and sometimes the dentist will miss the additional canal during treatment.  
Typical fracture does not have throbbing pain. Usually one cannot bite down on it. Or it hurts upon releasing from the bite force.  Throbbing pain indicates either a very advanced fracture or beginning of another root infection.

Root canal treatments are performed when a tooth is sufficiently decayed or damaged to have caused an inflammation or infection in the roots.  During the process, we essentially remove the soft tissue (nerves and blood vessels) inside, clean, disinfect it and expand/shape the canals as needed, to allow us to fill and seal them up well. If the treated tooth is a premolar or back molar, it will likely have two or three roots, each one containing one or two root canals. If any part of the treatment goes wrong-- either because root canal spaces were not accurately determined, the canals are not thoroughly cleaned and disinfected, or they are not filled completely and densely with an airtight seal-- reinfection can occur, causing pain such as the one you describe. Patients requiring root canal treatment ought to always ensure they are treated by an Endodontist who is appropriately trained and equipped to perform the treatment, or an experienced dentist, with top notch imaging, obturation and apex locating technology at their facility. It may seem costlier at first, but if it avoids re-infection, it is the always the safest, smartest bet.