When i got my cat from the breeder and brought him home he was in a terrible state with breathing difficulties due to a severe upper respiratory tract infection. My first experience with cats i was out of my mind with worry, i used to sit up with him at night with him struggling for breath. I understand the worry you must be going through at the moment. I cant remember which antibiotic we gave him, i will check when i get home this evening and message it to you as i have it all written down, the infection did take a long time to clear up as i remember but the important thing to know is it will clear up eventually and it does not neccessarily mean your cat will pick up respiratory infections it in the future, although it is widely thought that this type of cat are more prone to respiratory infections.
Another thing which helped was putting the cat in the bathroom with the shower running and putting a few drops Olbas Oil in the basin with hot water at the same time. Whenever i had a shower i used to take the cat in the same room and he just used to sit there breathing in the Olbas oil with the steam, it sounds mad but it really helped clear his airways.
Dont worry this will clear up your cat will need lots of quiet and rest, dont change the medication unless really necessary the infection will clear up, it just takes a while and while its happening you never feel its never going to go away. I think my cat took about 3 weeks to be properly over it, although he never stopped playing even at the worst point, cats are such brave little things!
Will message you the name of antibiotic later.
Thinking of you
Anna and Dexter the cat!