Simplest answer: Coughing can just be from a hairball or a kitty cold. These can be very common occurances in some cats. If you have some hairball remedy (or pea-sized ball of plain petroleum jelly), you could see if it helped (read hairball remedy label carefully for any contraindications and dosing suggestions).
More complex answer: You'd need recent lab work, listening to the lungs and heart, physical exam with thorough palpation of the internal organs and structures, maybe a urinalysis, and possibly an x-ray to get a good idea of what was going on ... in other words, a vet exam. Some of that you may have had recently; you can request copies of the results, although they might charge a fee for the copies.
If she'll let you, put an ear to her side and listen to her breathing. If you hear any crackles or wheezes, its a vet issue. If she ever seems to have any difficulty breathing, contact the vet.
Also, if you can, slowly massage your hands over her neck, back, chest, and belly, feeling for unusual lumps. If you find any, contact the vet.
Given the family history, I'd make the vet aware of it (as a reminder for him - its probably in the files there, somewhere), if you haven't already.
Note: Non-vets cannot officially diagnose illness in animals - that'd be practicing veterinary medicine without a license.