I have several facial piecings, three in my tongue, guages in my ears, etc....
--Peroxide is to sterilize and prep and area. Not for cleaning regularly. More for sterilizing new jewelry, that sort of thing...
--Neosporin, it does help with immediate problems, depends on what "camp" you're in. It's petroleum based, I don't fancy petrol being absorbed through my skin...
--Epsom salts, BIG WINNER!! Boil water for 20 minutes to sterilize, stir in appropriate amount of salt, flush/soak wound repeatedly with warm solution. If you can find a way to tip your ear into a cup of this solution, it draws infection out.
By the sounds of it, you had your cartillidge done with a gun and post earring?? If that is the case, imagine putting a nail on a pane of glass and then hammering through it. Your cartillidge shatters just like the glass. Then your body has to heal all those little cracks. It takes A LOT of time... some people just have a worse experience than others. Gentle cleaning with soap and water, and soaking it in epsom salts at least once a day is a good course of action. Light application of neosporin during the day between cleaning. And DONT touch it all the time! Your hands are covered with the normal filth of the day, scrub your hands before touching it. If you're able to get an earring in it, put a captive bead ring, or a horseshoe. Something that will not restrict the swelling. Some piercings can take MONTHS to settle down!
If you're cleaning and not picking, and you see continued swelling... or if you see not just the area right around the piercing, but more of your body (ear I assume) like your whole ear and part of your face turning bright red... it might be time to cry uncle and go to a doctor. Antibiotics do wonders for infection!