Thanks very much, your additional information is extremely helpful, I am very glad I asked additional questions.
I understand that it might be difficult but if possible I would like you to see if you can find where she defecates and check her stools. I suspect that they will be very normal, so this is more being complete than an absolute necessity.
What wormer was given, do you remember? Since she goes out and hunts more unusual parasites like lungworm do need to be considered. I would worm
any cat that goes out and hunts every 2-3 months with a broad spectrum wormer like Drontal (pyrantel + praziquantel). In cases where lungworms are possible we need to add fenbendazole (Panacur) too.
Since she seems to dry heave but never actually brings anything up, and this is very episodic, I too think you may be seeing more of a cough, or even more likely bronchospasms.
If she has an intermittent cough without any nasal or eye discharge a bacterial or viral infection seems very unlikely.
A dry cough can be a sign of heartworm disease. The most common symptoms for heartworm disease in a cat are coughing or gagging/vomiting. A simple blood test will help diagnose heartworm.
Another possibility, as I mentioned before especially since she is allowed outdoors to hunt, is a lungworm infection. These can be more difficult to diagnose but checking several stool samples for eggs or trying a course of fenbenadazole (Panacur) worming medication may be diagnostic if she gets better.
Of course the other possibility is feline asthma. We can usually diagnose them with radiographs of the chest when they are showing symptoms. But if we don't catch them during an episode radiographs can look clear. In her brother's case I suspect that the injection was a cortisone injection, which is exactly what is needed for asthma to quiet the spasming bronchioles. Asthma can run in families so she too may have it.
Heart disease is another possibility but I would her to be sicker with heart disease, and her cough to be more consistent. If she seems relatively normal otherwise, eating and drinking well, and active than heart disease is less likely.
It would be very reasonable to check a heartworm test as well as a stool sample and worm her with fenbendazole. If those aren't diagnostic and she isn't improving the next step would be to take chest radiographs and look for changes consistent with asthma and compare them to the previous ones taken to see if there have been any changes, if she has ever had radiographs taken before.
If her radiographs look suspicious for asthma or even if they look clear when she isn't coughing then try a course of bronchodilators (oral like theophylline or inhaled) and inhaled cortisone (like fluticasone). In most cases inhaled formulation of both drugs work best. In some cases your veterinarian may start with an injection of steroids to get her some immediate relief. Inhaled formulations can work directly on the lungs though, and thus tend to work better in the long run, and because they aren't systemic they have less side effects.
Rarely a nasopharyngeal polyp or a fungal infection can be the cause of a cough, so looking further with sedation and a nasal scope, as well as a look behind the soft palate may be needed, if she isn't coming along. With those things though I would expect a more consistent cough.
There aren't any good over the counter medications to give a cat with a cough, other than a wormer like fenbendazole, but hopefully I have given you the information you need to approach her cough and the diagnostic testing that will help pin the cause down and get her appropriate treatment.
Best of luck with your girl, please let me know if you have any further questions.