You never NEVER put rubbing alcohol on a piercing or any other open wound for that matter.. Rubbing alcohol will keep the wound fresh longer and double the healing process, and have more risk of infection..
You only clean it twice a day, before you sleep and when you wake up..
Dial works very well with cleaning it, but make sure there are no soap residue left.. Aside from listerine you can use sea/rock salt and warm water to gargle with or let a cotton ball absorb it and dab it on the outside part of your lip..
If there's a risk of infection don't take your ring off or it will spread on the inside just keep in clean and make sure your hands are clean, use the dial and the salt water treatment twice a day only..
If there is puss most likely crust will build up if it does just do the salt water treatment and don't peel anything off, you should be fine if you follow that, don't over clean because It's just as worse as not cleaning at all..