That's good that she's still eating and drinking. Is she's lethargic, then she might be running a mild fever. If you have a thermometer to take her temperature, then normal is between 100 and 102.5.
I'm not sure that her ingestion of inappropriate objects is necessarily related to her coughing although I suppose it could be (see #3 below). It's also possible that two separate things are going on.
There actually could be several possible explanations for her cough which I'll list below with some being more likely than not:
1. Kennel cough which is probably the most common cause for coughing in a dog this age. This condition is either secondary to a viral or bacterial infection and can be contagious between dogs. If a bacterial infection, then these dogs respond to oral antibiotics pretty quickly.
But if this is a virus , then it will have to run it's course....which is usually between 10-14 days.
Some of these patients will run mild fevers although not all of them do.
Kennel cough tends to worsen before it gets better and gradually improves rather than abruptly stopping unless this is a bacterial infection and antibiotics are started.
If this is kennel cough, then she may continue to cough for another week or so.
2. Canine influenza mimics kennel cough in the early stages as can pneumonia but these dogs rapidly become sick so not likely.
3. Ingestion of objects such as sticks or rawhide, grass, or anything that could cause damage to the back of the throat such as nuts. However, these patients aren't typically lethargic unless what was ingested (such as the carpet) has caused an obstruction; however, I'd expect her to be vomiting or not eating which apparently isn't the case.
If this is the problem, then it usually resolves pretty quickly…usually within just a few days if the patient doesn't continue to have access to the offending material. I recommend a diet of soft or moistened food (avoid dry kibble) so that further damage/irritation is avoided. You can soak any dry food which she might eat in water for 15-30 minutes which becomes like mush or oatmeal.
4. Problems with the heart whereby the heart can enlarge compressing the trachea and/or fluid is building up in the chest. Or heartworm disease which is transmitted by mosquitoes. It is possible that a good physical exam might detect a heart murmur or irregular heart rate. An x-ray and/or an ultrasound may be needed though to diagnose this problem.
5. Bronchitis which is similar to asthma in a person. These dogs are reacting to something in their environment that triggers inflammation in their lungs.. If this is the case, then control vs cure is what might be expected and the treatment is often different for each dog.
At her age, though, I'd have expected her to have had coughing episodes before now....which is true for collapsing trachea which can be seen in small dogs.
As to over the counter treatment options, cough suppressants can be given although I'm often hesitant to use them if kennel cough is the problem. I want those secretions removed from the upper airways and I rarely want to inhibit this reflex.
But acceptable ones to use include Dextromethorphan: http://www.petplace.com/article/drug-library/library/over-the-counter/dextromethorphan-robitussin-dm
The dose would be 0.25 to 1 mg/lb 2-3 times a day. You just want to double check labels and ensure that the formulations only contain this ingredient although inclusion of Guaifensin is fine.
If she continues to be really lethargic and/or she's running a fever and/or other symptoms develop, then a vet visit may be prudent. Otherwise, it may be ok to monitor her for another day or so to see if things improve.
I hope this helps. Deb