Louise,
What you describe can be a fractured root. A hairline fracture which can create a vector or pathway for more virulent bacteria to enter. This can cause the pain you are describing. Unfortunately, there are not good reliable tests to diagnose a root fracture. The only way to remedy the problem is to have the tooth extracted.
If I am uncertain of this being the problem, I will typically do a MyoralDNA test to determine if any high risk, moderate risk, or low risk pathogens are in a concentration above the norm. If so, it is a good indicator, barring no other areas of concern, that the tooth is likely fractured. If it is fractured, a root canal will not remedy the situation. If the tooth has not had a root canal, one should be accomplished, at the recommendation of your endodontist, as the tooth may be necrotic (nerve already dead or dying) and you are still receiving symptoms.
It is impossible to diagnose and recommend treatment in a forum such as this and you should only rely on a professional. If you wish to retain the tooth , you should probably see an endodontist firtst.

Hope this helps.