Cat has been breathing rapidly

've recently moved into a new place. This place is infested with fleas and has rats. About a day or two after moving in, I noticed my cat has fleas and he started rapidly breathing even at rest. He seems lethargic and seems to be trying to sleep all the time. He vomited once since moving in here; it was the typical greyish vomit that I've seen from him before. He also seems to pant at random times with his mouth open. His appetite seems alright; he's been eating and I've spotted him drinking water. I took him to the vet; after taking his temperature, looking at his gums, and listening to his breathing, they recommended xrays. Got xrays done and after stating that he has asthma, gave a depo injection. It's been 24 hours since then, and nothing has changed. Couple weeks ago I had gone in and he was diagnosed with a possible UTI; gave the cat the recommended medication over a span of a week and he seemed completely fine. Called my vet again and he said to keep an eye on him.

I've ordered Advantage II to get rid of fleas and it should arrive soon. I tried spraying Apple Cider Vinegar on him but am unsure how much it helped. He definitely didn't like it. Could the fleas actually be causing this? Anything else I could do? He's lived with my parents before for about a month, so I couldn't imagine the move having an effect on him.

Here's a video of a rapidly breathing cat. I'd say my cat is breathing about twice as fast at the moment

Time his breathing. A normal cat breathes ~30x a minute. One of my cats had an issue with rapid breathing and it turned out to be pulmonary edema...but this is probably unlikely. You really should take him to an emergency clinic if he is breathing more than 60x a minute. If I had to guess, he needs some albuterol and may have developed some asthma if you just moved to a new place. Have you noticed him coughing at all there? (sounds like coughing up a hairball). He appears to be in respiratory duress, please consider taking him somewhere. You may want to keep him at your parents house until the apartment is clear. The droppings from the flies and rats can be really irritating to breathing.

I really hope you have the windows wide open and are ventilating your apartment well. You might come down with issues too. 

Also, did you do anything new to him today?