When we look down we can do so from the base of the neck OR from the top of the neck. Try nodding your head just from the top. You will see that a good amount of flexion can be achieved. While there is a need to crane your neck to some degree in the early phase of feeding. I would suggest that once your baby has started feeding you pull your head back and try to just flex from the top of the neck instead. This way you will avoid the build-up of tension that occurs at the base of the neck.
Additionally, chiropractors and physiotherapists both have many simple exercises that can help relieve this discomfort so if you are getting prolonged neck pain and headaches while feeding your child, consult your family chiropractor and they should be able to help.