Ever since I had my first daughter three years ago, I've had pain on the right, back side of my neck, lessens if shoulders are down?

Muscle compensation. It sounds like you have been compensating through your upper back, arms and neck since having your child (from holding her, daily child activities, postures etc). I would recommend seeing a physical therapist who can evaluate your posture, movement patterns, and muscle imbalances. From there he/she can provide treatment and give you a home program to help yourself.
Chronic trigger poin. Massage trigger point injection baby sling may help strengthen after pain goes away to avoid next one.