Thanks so much for the additional information.
Gum color is normal which is good. Her respiratory rate is obviously quite high since normal (at rest) would be between 20-30 breaths per minute. This is somewhat concerning that it is so elevated.
I have several thoughts as to what's causing her lethargy and increased respiratory rate:
I understand about not having a thermometer but if manage to get your hands on one, it will be quite helpful in knowing what her temperature might be. Normal is between 100 and 102.5. If it's normal, then a fever can be taken off of the problem list but if it's high, then we have an explanation for her behavior.
Of course, then we'd have to wonder why it's high. Possibilities range from a bacterial infection (possibly secondary to an abscess), viral diseases (such as Feline AIDS, Feline Leukemia, Feline Infectious Peritonitis), toxoplasmosis, an early upper respiratory infection....to name a few possibilities.
There's also a condition in cats that is called Fever of Unknown Origin--this is exactly what it sounds like which is that we can't find an explanation for the elevated temperature. Treatment is primarily supportive which consists of fluids and drugs to reduce the fever. Most cats recover very quickly.
2. She could have a cardiovascular problem which, given her age, would be secondary to basically a birth defect or problem present at birth which has caught up with her.
It's possible that a thorough physical will pick up a heart murmur or abnormal rhythm but usually other diagnostic tests such as an x-ray or ultrasound are needed.
If this is the problem, then we have very effective medications which can be given and many patients can do reasonably well for long periods of time (depending on the diagnosis, of course).
3. Cats with primary respiratory issues such as pneumonia can behave as you describe. Pneumonia isn't a common problem in cats (as opposed to dogs) but when it does develop, it's usually caused by a bacterial infection (so antibiotics are usually prescribed).
Again, a physical might pick up changes in the lungs but an x-ray will be more diagnostic.
4, Pain can cause an increased respiratory rate but I wouldn't necessarily expect her to be as lethargic as she is. And, if you can't localize any areas of pain when you touch her body, then this is less likely.
5. If she had simply overdone it, playing really hard outside, then I might expect her to sleep more than normal but I wouldn't expect her respiratory rate to be this elevated.
I'd love to be able to advise over the counter medications for her but it wouldn't be considered advisable or safe to give her any drugs since cats are so sensitive to many of them and they could cause more harm....certainly without having a better idea of what's causing her symptoms.
Maintaining hydration with water or Pedialyte is important, especially if there’s a fever so encourage her to eat...perhaps wet food (if she likes it) since it contains more water. You could also ask tuna or clam juice to it which will increase her fluid intake.
If she continues to behave tomorrow as she's behaving today, then a vet visit may be prudent.
I hope this helps and that she's feeling better soon. Deb