Why do you have a cat if you are willing to deny all vet care to the poor cat? Surrender it so it can get a non lazy home and get some one who will CARE for the cat
It's hard to say what it will cost you. Vets costs vary from clinic to clinic and they also vary according to what country you're in and what area of a country you're in. In many areas of the USA, low cost shots are available. Since your cat hasn't had shots yet, vets probably will insist on giving her the necessary shots in addition to treating the conjunctivitis.