She came back with a swollen arm two days ago, but she's now eating and drinking normally and the swelling has gone down ~80 percent. She keeps licking the area.
It looks possibly like a ruptured abscess. She should definitely get checked out by a vet. In the meantime can you put an e-collar on her so she can't lick it?
It looks like your Kitty might have gotten into a fight or rec'd an injury, which became infected. Often they will swell up and cause pain...cats will instinctively lick the area and often will cause it to rupture and drain. If the wound seems to be free from drainage and doesn't smell, the wound might be healing on it's own. If it is still swelled, causing obvious pain, red, or smelly, then a trip to the vet is in order. If it is an infection, a Vet will usually open it, allow it to drain, and irrigate it with Hydrogen Peroxide to get rid of the infection and clean out the wound. This isn't unusual in cats, who like to fight sometimes.
As far as licking goes, some will recommend an Elizabethan Collar (E Collar) to prevent licking, while some would allow the cat to lick it. I guess it depends on the reasons and circumstance, but in the wild, cats would lick it until it is healed unless they lick too aggressively and cause the wound not to heal.