Hello, my name is***** and I have over 20 years of experience as a veterinarian. I'm sorry to hear that your girl is sneezing, has eye discharge and isn't eating well.
I suspect that she has picked up a contagious upper respiratory infection. An upper respiratory infection in cats is just like a cold in you and I, and these are commonly caused by a virus, the most common one being Herpes virus. These are easily caught by breathing in virus particles in the air from a sneeze or nasal or eye discharge. Some cats get sicker than others and young, healthy adult cats seem to tolerate them and fight them off better than very young kittens or older cats.
You can help her feel better by adding warm water to her food and warming it in the microwave for a short time to make it smell more (they don't eat if they cannot smell) as well as making it easier to swallow.
Also the more fluids she gets the better. Offer tuna juice, and low salt chicken broth, run the tap if she likes to drink out of the sink.
Take her into the bathroom with you if you run a hot bath or shower as the steam will soothe her sore throat and airways and thin the mucus in her airways making it easier for her to breathe.
If her nose become very congested you can use sterile saline to loosen the thick mucous and remove it. She won't like it but it will help her breathe and be able to smell her food better. You can also use sterile saline to remove eye mucous if it accumulates, then apply artificial tears every couple of hours to keep her eyes hydrated and comfortable.
You can give her an amino acid supplement called L-lysine at a dose of 500mg orally twice daily. If this infection is due to Herpes this amino acid interferes with virus replication and will shorten the infection's duration and severity. Good supplements to try are made by the Viralys brand which comes in a powder to add to the food or a tasty gel.
Don't bother with emergen-c powder or any of the supplements with vitamin C that we take when we have colds. Unlike us cats have the metabolic capability to produce their own vitamin C and any excess we give won't be helpful. Vitamin C is a gastrointestinal irritant and will only interfere with her appetite.
Some lethargy is understandable, let her rest as she needs rest to get better. If your cats normally go outdoors keep her (them) inside until they are back to their normal playful selves.
If she runs a high fever (more than 104F), has a green or yellow nasal or eye discharge, stops eating even with coaxing and clearing her nose and eyes, or starts coughing or having difficulty breathing then she needs a veterinary exam. Not an emergency as long as she is eating but soon if she isn't eating or has a green or yellow nasal or eye discharge.
Sometimes these upper airway infections turn into pneumonia so that's what we need to guard against. In most cases antibiotics aren't needed and can contribute to a decrease in appetite so I don't tend to prescribe them unless I feel there is evidence of a secondary bacterial component. These include a green or yellow eye or nasal discharge, evidence of pneumonia upon listening to their lungs or an infection that lingers beyond the normal 10 or so days.
I highly recommend testing her for feline leukemia and feline immunodeficiency viruses if her respiratory infection lingers. These immunosuppressive viruses will make a simple infection much worse as they stop the immune system from fighting infections the way it was designed to do.
Other reasons for sneezing and nasal congestion are an infected tooth root, a fungal infection, a foreign body inhaled into the nose or a nasal polyp. If she isn't improving at all in 7 to 10 days she needs a veterinary visit.
Let me know if you have any further questions.