Sometimes people take drugs to fight coughing and a stuffed nose. I used to, until I realised that many drugs that fix the cough actually make the stuffiness in the nose worse. If your nose is very dry I suggest buying a cheap saline spray from a chemist to moisten the nose, this is cheap and is almost like salt water. Use it in the morning and at night. If that doesn't help in two days then you could buy a nasal rinse unit, which does a similar job but keeps all of the sinus area clean. This should be used once a day in the morning and not before you go to bed.
Better in my opinion to have a clear nose and a cough rather than a stuffy nose and no cough. At least until you see a doctor.
Sorry about your predicament. If you can find vicks vapo rub you could put some under your nose and on your chest. Is your cough dry or loose? If loose cough honey in hot water or herbal tea? If dry cough steaming yourself over a hot water pan (but don't knock it over or burn yourself!). Breath in the steam and it will make you cough and that is good if it is a dry cough. I don't know how well those sticky things you put over your nose to open your nose that you can buy. I am not sure of the name of them. They pull your nose open. But menthol and honey-lemon cough drops with menthol and that kind thing helps a little. If you develop a fever see your doctor though.