Do we need to head to the pediatrician if my 4 month old has a runny nose? She doesn't seem bothered by it, no fever, it is making it hard to bf.

Not necessarily. Try saline drops in the nose, followed by suctioning, just before feeding. Babies can't blow their noses, and need to breathe through their nostrils during feeding. If runny nose is the only symptom, you're ok to treat at home.
Runny nose. A runny nose by itself is no cause for alarm. Often it iscaused by a virus and will resolve in a week or two. Using saline nose drops to thin the secretions and clearing the nose with a bulb syringe will help with breastfeeding.
Maybe. Try clearing her nose with your bulb syringe, and using either a humidifier or take her into the bathroom, turn the shower on as hot as it will go, and let her breathe in the steam. If not better, see your doctor.