If you get warm water and dilute some salt into it until it's actually past the point of nasty, like really dissolve it til it's mostly salt water then swish with it it'll kill germs and bacteria.
If you use hydrogen peroxide, like 1/5th peroxide and 4/5 water, that'll also help kill the bacteria which will in turn help it heal.
Sometimes split gums are caused by food that had skin grow over it and then dislodges, ripping the gums. Brushing them with a finger once a day will stimulate growth in your gums and you can start to heal, but you'll never heal unless you pick a method of keeping it clean.
Listerine works, but I figured I'd offer non-easy-answers since Listerine should be the "Duh" answer.
Rubbing alcohol is right out, don't use it. Not only will it give you a tummy ache to swallow, but it'll make you trip balls for a few minutes in a brain-cell-not-feeling-good kinda way. Take it from experience...salt-water, peroxide, or listerine are your best methods of keeping your gums clean long enough for them to heal.
Btw, rubbing your gums lightly is part of the key to healing. Your saliva will heal it quickly, mouth wounds don't take long to heal, but rubbing it alerts the brain of that part of the body and pays closer attention to it in all aspects.
If you have any more questions don't hesitate to PM me :D