Why does my root canal still hurt after 3 months?

Pain after 3 months. A root canaled tooth will feel different that a vital tooth. However pain after 3 months may indicate that the dentist or endodontist may have missed a canal or the tooth and/or root may be cracked. Best advice would be to return to the treating dentist and ask them.
Infection. If a tooth still hurts after three months of having a completed root canal there can only be three reasons: a- infection b- poor done root canal c-fractured tooth have it evaluated by your dentist.
Root canal . Root canal therapy is not a slam dunk, if a tooth is still hurting 3 months later it may be due to infection, fracture in the tooth, incomplete instrumentation and removal of nerve tissue and debris, leakage in the seal. Was the tooth crowned or simply filled does the patient clench or grind, what condition was the tooth in prior to the root canal treatment, there are more than 3 variables.
Many causes. Possible infection, fracture, accessory canal, or inflammation. Have your treating dentist re-evaluate the tooth and surrounding bone.