Gum color should be pale pink so this sounds normal.
Respiratory rates at rest in a cat should be between 20-30 breaths per minute so this also sounds normal.
Thank goodness he urinated so that we can take a urinary blockage off of the list.
When the third eyelids are elevated, this can often be a non-specific sign of illness in a cat although it can reflect other problems as well such as uveitis (inflammation of structures in the eye), early upper respiratory infection, Idiopathic (we can't find an explanation for it)...among other things.
As far as explanations for his lethargy and disinterest in food (and what appear to be balance issues), there could be several possible explanations for this behavior as well:
1. He could be running a fever. I understand about not being able to take his temperature but if you do manage to take it, normal is between 100 and 102.5.
Of course, then we'd have to wonder why the temperature is elevated if it is. Explanations for this could be a viral or bacterial infection.
There's even 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.
Toxoplasmosis is a bacterial infection which can affect the eyes and also cause balance issues so this may be something to definitely consider if he goes outside or even if he doesn't. Cats primarily contract this disease by eating rodents or birds and I've diagnosed indoor cats with this condition (likely from ingestion of mice who got into the house).
The prognosis is good for most cats once they've been started on antibiotics such as Clindamycin.
2. Pancreatitis can happen very suddenly and these cats just stop eating and can become lethargic but these patients don't usually have balance issues. We don't have a good explanation for why this happens, either.
We do have several tests for this condition although I've come to doubt their reliability in some cases; treatment consists of fluids and pain medication (we believe the pain is why they stop eating).
3. I probably should include other systemic diseases such as problems with the kidney, heart or autoimmune diseases on the list but they're not as commonly seen in a cat this age as the ones mentioned above.
4. I'll mention toxicity of some sort since cats can develop balance issues when either prescription, otc or illegal drugs are ingested.
Often gi signs are also present (such as vomiting) but not always.
As to over the counter treatment options for him, it's not considered advisable or safe to give cats any over the counter drugs since cats are so sensitive to many of them and they could cause more harm.
Maintaining hydration with water or Pedialyte is important, especially if there’s a fever. You can dribble this into the side of the mouth with an eye dropper or syringe every several hours if he's not drinking. I don't think you'll need to force feed him since he hasn't been sick for very long.
But, if he's truly acting disoriented and having difficulty walking, then a vet visit may be prudent.
I hope this helps. Deb