The data you have given is not sufficient to reach a definitive diagnosis. Was the tooth infected and/or operated for a root canal treatment
before the crown placement? How long has it been since the RCT/crown placement done?
For now, with the data given, i would guess it might be due to a periodontal abscess
in the region. And if there had been an infection and RCT was done, chances are infection may not have resolved completely before the obturation which may have caused a periapical cyst
or an abscess. A radiograph of the tooth is needed to confirm/rule out the diagnosis. If present, it may require an antibiotic and anti-inflammatory treatment and if that doesn't work you may need to get your RCT redone.
Either case you will need to visit your dentist
to get a clear picture.