Hi:) My son just went through is first cold as well, no cough, but disgusting snot for a week! Saline nasal drops are good (Little Noses has a kit you an get with drops and an asperator if you don't have the one form the hospital). The isn't much you can do for cough, there is little evidence that cough meds work in adults and no evidence that they do for babies. Really, you don't want them keeping anything in their lungs, you want them to cough it out. Just keep things warm and humid, give her a bath after you take a shower so the bathroom is nice and steamy but her bath water isn't.
Good Luck!