I have a 7 year old calico kitty who has developed a deep cough. She is eating fine and drinking and going to the bathroom. I do not know if it is allergies or maybe a hairball. What can I do. I can not aford to take her to the vet for x-rays.

Take her to the vet. Work out a payment plan if you must, you owe it to your cat to take the proper care of her.

If you can't afford medical care for your cat, you should surrender her to somebody who can. Sariss is right... try to work out a payment plan if you can't pay all at once.

Vet will probably not need to x-ray.

A deep cough could mean something like CHF, so you can't say they "probably wont".