I have had an increasingly sensitive tooth. is this a cavity?

Usually iis a cavity: Increasing pain usually nindicates a cavity has formed and it is getting close to the nerve. If not treated asap it usually requires a root canal and a crown. Pain can get severe if not treated soon.

Maybe: May be a cavity or may be gum recession, crack in a tooth or filling. Let your dentist take a look. You could avoid major work if now its only a small filling.