Asthma is the first thing I thought of when I read your question and would likely be the most common cause for her symptoms.
I can understand why you might think that the plastic she chews would be related but I think it's not likely to be the case.
However, in my experience, Depo Medrol tends to work longer than a week for most patients. So, either her condition has progressed to the point where she might need an inhaler (such as Aerocat) to control her symptoms or possibly other drugs such as a bronchodilator or something else is going on with her.
The other possible causes for coughing in a cat include:
1. Bordetella or mycoplasma infections although typically these cats aren't coughing with the pattern you've described.
But, if/when I suspect that it might be present or complicating the situation, I'll dispense Doxycycline 5mg/kg twice a day which also has the benefits of anti-inflammatory properties
2. Lung worm which is a parasite that is most often diagnosed with a fecal sample This condition would be less likely in an inside cat. One effective treatment would be panacur.
3. Heartworm disease. This disease is transmitted by mosquitoes and depending on where you live, may be a possibility. We do have a test for this condition which is often done in a vet's office. Unfortunately, we don't have an effective treatment for it in cats like we do in dogs. This disease is different in a cat than in a dog and the coughing is related to inflammation in the lungs.
Steroids can be used to treat this inflammation.
Cats can develop a condition known as heartworm associated respiratory disease (HARD) which can result insignificant damage to the lungs and resultant symptoms such as wheezing and compromised respiratory function. These cats are typically negative when an antigen test is done but often positive when an antibody test is run. Ultrasound is normal with no worms detected. Radiographic changes are usually detectable helping with the diagnosis but you have to know what you're looking for since those changes could be confused with changes secondary to lung worm or migrating rounds worms or possibly asthma.
Unfortunately,we don't have effective treatments for this condition either although steroids can be effective in helping to reduce inflammation and the accompanying symptoms.
4. Heart disease. These cats usually have other signs in addition to coughing such as weight loss or exercise intolerance. Stress might trigger a worsening of the condition.
A chest x-ray can be useful in determining if there is an enlarged heart or fluid in the chest but ultrasound is usually needed to determine the exact diagnosis.
If she were my patient and wasn't responding as I expected, then the next step that I'd suggest would be a chest x-ray. If there's any question about what may or may not be seen, then a specialist could be asked to evaluate them.
I'm hesitant to advise or suggest any otc medications until or unless we have a better idea of what else may be going on; in any event, many otc drugs aren't safe to use in cats like they would be in dogs.
I hope this helps to provide additional options for you to consider. Deb