Tooth sensitive after having a cavity filled. is this normal?

Not uncommon: Drilling and filling a tooth is actually a minor surgical procedure on the tooth. The nerve of the tooth becomes temporarily inflamed and may cause resulting sensitivity. If the filling is slightly 'high', the living tissue that surrounds the root of the tooth may become inflamed as well. This would require your dentist to adjust the bite.

It can be: Teeth can be sensitive after a filling. See your dentist to evaluate if the filling is too high. Was the feeling deep, this can cause sensitivity. Sometimes tooth colored fillings cause more sensitivity than silver fillings.

It's not unusual: It's not unusual to have a little sensitivity after a filling is done. It shouldn't last too long though. If it is persistent for more than a day or two then you should see your dentist. It may be as simple as adjusting your bite or it could mean the tooth may need more extensive treatment.