The gum line gets swollen because food debri and plaque easily accumulate on the
fractured tooth causing inflammation (bleeding + puffiness) of the gum.
You should do your best to keep the area clean. Gently taking a tooth-pick and use it to
wipe the surface of the tooth near the gumline...
Sure sounds like an infected and/or dying nerve. A root canal will solve the problem. After, the tooth can be bleached, veneered, or crowned