Thank you for your question. I am sorry to hear that you discovered recently that you have a fragment of your left wisdom tooth left behind by your previous dentist.
I can share with you that from my experience, even in the best surgeon's hands, leaving a small tooth fragment behind is not an unusual occurrence, especially if the surgery was a difficult one involving cutting the wisdom tooth into several pieces.
Most of the time, a small broken tooth fragment left behind does not give any problems at all but in a small percentage of patients, problems can arise.
From my experience, it is unlikely that your headaches are related to the wisdom tooth fragment, but i have learnt never to say never, because with human biology, things happen that sometimes even surprises the most experienced of doctors.
In my practice, i have only ever had one patient with similar symptoms to you, and when I helped the patient remove the tooth fragment, her migraines went away.
Depending on the location of the tooth fragment as seen on an Xray, your dentist can attempt to remove it either surgically or non-surgically.
I would recommend that you consider going back to the dentist that did the surgery for you in March 2017 to discuss on the best way to remove the broken fragment. He would know best since he is the surgeon that took the tooth out for you!
After the fragment is removed, if you still suffer from headaches, then you can deduce that the headaches are most likely not caused by the fragment.
I hope this information is useful to you and I wish you a speedy recovery from your headaches!
Dr Gerald Tan