If you have a suction cup, empty the runnies before you give the breast or the bottle. There are some very serious viruses going around right now, so don't be afraid to call the pediatrician for guidelines.
Within the realm of cold symptoms, runny is good. Stuffy is bad. Did your pediatrician's office give you handouts or a booklet with basic information on childhood illnesses, recommended treatments, and when to call the doctor?