Sick Kitten! What is my kittens diagnosis? How can I help her?

I just bought a young kitten and when I got her I found feces on her foot and she had fleas. I don't know her age so I am scared to use any flea medicine however I have bathed her twice. The first time was to try and kill the fleas. Everyone in my house said she smells so I washed her again with a better smelling shampoo and she smells better. For the first couple days I fed her cat food and she was puking the first two days but I got her kitten food and she stopped vomiting. I found out she had diarrhea and when she went to the bathroom she meowed intensely. Her eyes are starting to form yellow and green goop in the corners and today i noticed she has redness around her eyes as if she put on red eyeliner. I have only gotten her first vaccine and I dont know her age either. She is about a pound. I have treated the diarrhea with some pink liquid over the counter medicine from Petco and she has solid feces now. Can you help me figure out what is wrong with her?