One sign of asthma in cats can be a cough. It is often a dry sounding cough (almost like a hairball) and when the cat coughs their head is stretched out and they are crouched down parallel to the ground. Asthmatic cats may also wheeze from time to time, but not constantly. There are also several other reasons for coughing such as parasites and infectious disease. I would recommend that your cat see a veterinarian. They can do a complete physical exam and pay special attention to how the lungs sound, although an x-ray may be needed to determine if asthma could be causing the cough. Asthma can be a serious condition and cats can have extremely serious asthma attacks like a person would, so if you are concerned better to have her checked out sooner rather than later. Take care and let us know if you have more questions.
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My cat is 6 months old and she makes weird sounds - something like she was coughing. 
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