Certainly a cough of any type that has continued for that length of time is going to benefit from medical help, especially if it does not seem to be decreasing in intensity or frequency. Home care measures that may help are using a humidifier or steamy bathroom 15-20 minutes 2-3 times daily and also ask your pharmacist to point you to straight guaifenesin syrup and start with 0.1ml per pound of body weight orally 3 times a day. With the duration of the cough you might want to check with your veterinarian about using an antibiotic also, I prefer doxycycline, zithromycin or a cephalosporin. Hacking, gagging coughs are a sign of irritation in the pharynx or back of the throat and can be caused by physical irritation from chewing on stuff but with the duration of her cough this is not the likely cause. Please let me know if you have other questions.