The only thing that I suggest is that you borrow a live trap from your local animal control office or humane society. You will need to trap her and get her to the vet. Mouth problems can signify a lot of causes, including FIV and FelV, two contagious diseases. So, do take this seriously. If she is drooling, she could have an abcess or other mouth issue.
If you have trouble finding a trap, you might want to try a couple of cat rescues and see if they will help you trap her. They might even be willing to spay her for you for low or no cost before you release her again. You can find cat rescues in your area by going to www.petfinder.org.
Let me know if you still have questions.