What can I do for my runny nose without going to a doctor?

Runny nose. Runny nose is just a symptom. It usually comes either from a cold or from allergic symptoms (usually lasting longer than 3-5 days). Allergies usually respond well to otc antihistamines like Claritin or claritin-d. Cold symptoms tend to be more profuse, and the best treatment is with otc nasal spray like afrin, but you can't use it for more than 3 days, or your nose gets hooked on it.
Drippy nose. Runny nose could be from allergic or non- allergic rhinitis, tobacco exposure, colds... Use of non- sedating antihistamines can be helpful but due to the fact that they are devoid of anticholinergic effects, they do not do much for the rhinorrhea. Addition of an oral or intransal decongestant can be helpful but watch out for rebound congestion.