Broken Tooth Down to the Gum Line Swelling and Filling Up with White Stuff What Should I Do?

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 will help remove the plaque in the area.
The area may bleed initially, but continue to keep the area clean.
To keep the inside of the tooth from filling up with debri, do salt water rinses.

But you need to go to the dentist to have an x-ray done.

Somtimes if the tooth is broken down to the gum line, it can still be saved by doing a
root canal, and a post to hold the core/crown structure of the tooth.

If it's determined from the x-ray that there isn't enough bone anchorage for the tooth,
tooth should be extracted.

I hope I answered your question!