My 9 month old has a runny nose....How can I clear it up without going to the doctor?

Lots of ways. Placing a humidifier in the room can help loosen up the mucus, playing, nursing or feeding your baby in a warm steamy bathroom may help. Also, putting saline drops in the nose and using a bulb suction to suction out the mucus will help clear the congestion.
Runny nose. For 9 month old, put saline drops and suction the nose, give plenty of fluids, also keep a humidifier in the room she sleeps. Something neat I learned- rub Vicks vaporub on the soles of his feet and put cotton socks, the cold cleares up faster.