hello and welcome to HCM forum,
i would like to inform you that the kind of sensitivity you are facing is due to the nerves which are exposed , initially it was an acute condition but now it has become chronic, therefore you are experiencing pain which does not subside even after taking medication, i would recommend you to visit your dentist
and get the tooth checked thoroughly, most probably root canal treatment
will be the line of treatment, but confirmation will be done after looking at the x-ray of your tooth.
i wish you good health,