I was waiting for you to respond to the chat, I had some questions:
How does your cat's color of the gums and tongue look? Pink, pale or blue?
Has she had any coughing or sneezing?
How long has the breathing problem been there?
Does she breathe fast or noisy?
All those signs seem to point to a serious condition. The labored breathing can mean either a heart or lung problem. If it is just fast breathing that can be due to a fever. The clumps in the hair usually mean that they are feeling bad, don't fee like grooming. I would at least take her temperature and see if she has a fever. If she does this can often be remedied with antibiotics. If she doesn't she's probably got something serious internally going on. You can place a thermometer in the rectum for one minute (put vaseline or K-Y on the end of it). 103F and up is a fever; normal is 100.5 to 102.5. If it is lower than 100.5 that is not a good sign, either.
Let me know if you have more questions.