There's only a little pain but swollen enough to annoy

Who diagnosed it as an abscess? If you don't want to see a dentist, it sounds like you did. If it is one, I can't think of a home remedy.

But the fact that there isn't much pain might mean that it's rotten food stuck between the tooth and gum, and that can have home remedies, starting with gentle brushing (soft bristles!) and flossing all around the tooth, and use a proxibrush too (a tiny 'bottle brush'). Rinse many times a day with hot salted water, swooshing vigorously. If that hasn't helped in 2 or 3 days, you must see a dentist. Go to a clinic if you can, for sliding scale costs.

It isn't food making it swollen - it's blood rushing in with cells to fight off infection. If a lot of blood comes out when you floss etc, you have a localized case of gingivitis.

That's IF it isn't an abscess!

And eat using common sense - no foods that might get stuck in the gum, chew on the other side, and rinse after every time you eat.

If you know it is abcessed, then you have had diagnosis right?

There is NO home remedy. No amount of brushing, no amount of salt water will make it better.

If it is abscessed, the infection is coming up from the bottom of the tooth, trying to exit at the top causing the pain and swelling.

See your dentist again and have him deal with it!