hello and welcome,
your tooth has infected either due to improper root canal treatment
or due to a improper crown placement.
visit your dentist
and get an x-ray to rule out the cause.
try to maintain the capped tooth hygienically as there is more chance of plaque
use soft inter dental brush to prevent accumulation of food debris.remove the cap by your dentist and get your teeth cleaned.root planning also can be done if there is subgingival plaque accumulation.
if there is still vital pulp remaining after the rct has done,re-rct has to be done to remove the remaining vital pulp tissue as it can cause pain and periapical inflammation.
take tab.doxycycline-100 mg once a day for 7 days to reduce gingivitis
the swelling can also be due to gap between the teeth ,which can be corrected by restoration,tissue grafting.
get scaling done in every 6 months.