Sometimes cats cough because they are allergic to their food.
A rescue organization may be able to help, some have volunteer Vets coming in on certain days.
street cats are very prone to upper respiratory tract disease, a broad category of viruses, including herpes and calici. they fall under the umbrella term of URI's.
the best way to treat these is by supporting the immune system...(unless it turns into a bacterial infection than they need an antibiotic)
you start her on an amino acid supplement called L-lysine...this will support the immune systems and help prevent any flare ups(cold like symptoms) Every Vet I know recommends this.
I will give you the product name, you can use this brand in the human line rather than the more expensive and lesser quality ones available thru your Vet clinic.....ask for this brand at your local health food store or vitamin supply outlet, if they don't carry this one than you can order it online from iherb a very reputable company I deal with all the time...it comes in powder form,.they can use 250 mg per day... thats 1/4 of a scoop..(thats included) in their wet food. it is very inexpensive, only $6.43 plus $4 shipping, if you use this code on your first order you will get a $4 discount. so this is very affordable.
Boy Opus is not the "Big Cat" here for nothing. Everytime I want to say something she has already covered it. Thank God we have her.
Only thing I can ad is my kit has the herpes virus , part of that URI Opus was talking about. Stress is a major catalyst for these kinds of outbreaks--they are basically Kitty Colds. IF the disharge from her nose or eyes becomes yellow or bloody then she will need to see a vet for antibiotics. This means it has become a bacterial infection that needs meds.
The first thing as a furbaby Mom is cancer, I was so afraid to take her to the vet for fear of this news, thanks for the help, I will obtain the llysine today