I think my 3 month old baby has a cold. she has a runny nose and a wet cough. there are no signs of a fever. should i be giving her medication?

No: The first months are troubled by narrow nasal passages & exposure to dust, fragrances, smoke & other irritants.Baby tries to flush these out of the nose with mucous but this often ends as congestion & produces rattling & cough. The best rx is washing out the nose with saline & suctioning the remainder. There are no meds that help at that age.