Thanks for the additional information.
The antibiotics are what I'd have dispensed if I suspected an upper respiratory infection or Feline Flu which is why I'm assuming your vet dispensed them for you to give at home.
I don't like it when a cat open-mouths breaths, but if he's showing improvement with this symptom, then the antibiotics must be helping.
Wheezing and open mouth breathing as you describe can also be secondary to asthma; however, these cats typically won't respond to antibiotics (they need steroids) so this is less likely to be his issue. Heart disease can also cause open mouth breathing and lethargy but, again, is not usually responsive to antibiotics.
I suspect that he has Feline Flu which often gets worse before it gets better. But I do have a few additional suggestions for you which may help:
1. Nasal decongestant drops can be helpful although many cats don’t like them very much as you can imagine. The medicated ones should only be used for three days in a row, with one drop in each nostril; otherwise what’s known as a rebound effect may occur
a. Pediatric otrivin=0.05% xylometazoline
b. “Little Noses" Decongestant Nose Drops with phenylephrine hydrochloride
c. Afrin (oxymetazoline)
d. "Little Noses" Saline Spray/Drops non medicated which can be used more than three days in a row.
3. You can place him in a bathroom with hot water running so that the steam can loosen up secretions or place him in a room with a dehumidifier to moisten the air.
4. Antihistamines can help some cats but I might be hesitant to use them in this case because they can cause sedation. We won't know if he's getting worse or if he's only having a side effect to the drugs. But ones which are safe include:
Diphenhydramine at a dose of 1/2 of a 25 mg tablet given twice daily or
Chlorpheniramine at a dose of 2-4 mgtwice a day or
Loratadine (Claritin)at a dose of 2.5-5 mg twice a day
It is important to ensure that the formulations used contain ONLY the antihistamine and are not combination products (e.g. Claritin-D contains pseudoephedrine, which could cause very significant adverse effects in a cats.
5.Force feeding is sometimes necessary in these cats if they aren’t eating.You can mix canned food (or human baby food but avoid onion and garlic formulations) with a lot of water in a blender and use an eye dropper or syringe to squirt some of this liquid into the mouth.
I hope this helps and that you see improvement soon. Deb