Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry that your girl Piper isn't feeling herself and is sleeping quite a bit and not eating and drinking as usual.
Is she running a fever (rectal temperature greater than 103F)?
Any sneezing, nasal or eye discharge?
Any vomiting or diarrhea?
In a young cat that is very lethargic and not eating well the most common cause is a viral infection, usually an upper respiratory infection, which are similar to a bad cold in you and I.
I would start with an acid reducing medication to try and settle her stomach and get her eating and drinking. You can give either:
1)Pepcid ac (famotidine) at a dose one quarter of a 10mg tablet per 5 to 10 pounds of body weight every 12 hours
2)Prilosec (omeprazole) at a dose of one quarter of a 10mg tablet per 5 to 10 pounds of body weight every 24 hours.
These are acid reducers which will decrease irritation of the stomach and esophagus and should help her feel better, and hopefully get her eating. They can be used for several days if need be.
You can help her feel more like eating and improve hydration by adding warm water to her food to make it smell more (they don't eat if they cannot smell) as well as making it easier to swallow if she has a sore throat.
Also the more fluids she gets the better. Offer tuna juice, low salt chicken broth, run the tap if she likes to drink out of the sink. If she continues not to drink you do need to continue forcing water every few hours with a syringe.
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.
If she is sneezing and 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.
If she is sneezing you can give her an amino acid supplement called L-lysine at a dose of 500mg orally twice daily. If this is an infection and is 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.
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, continues to not eat 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 starts 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 7 to 10 days.
I highly recommend testing him for feline leukemia and feline immunodeficiency viruses if his 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.
Let me know if you have any further questions.