I am sorry your girl is having trouble.
Does she go outside?
Any chance she got into anything toxic including human medications and plants?
What color are her gums?
How long has she been like this?
Is she spayed?
Can you take a rectal temp?
Ok This is an emergency cats do not open mouth breath unless they are not getting enough oxygen.
Once a cat starts open mouth breathing the is only a very short time frame in which to get them help. The signs you have described sounds like some type of toxic ingestion, or a problem with the heart.
I would suggest getting her to your local animal emergency immediately. If she is not seen right away I am afraid you will loose her.
If you need assistance locating an emergency hospital in your area please supply your zip code.
Please know that time is of the essence here so she must be seen right away.