How could I know if I had broken any bones in my neck?

Neck. Typically a fall or significant injury are needed to fracture bones in the neck. If you have pain in your neck and you had an injury like this you see a doctor today in the er. After examining you, x-rays may be done as well as a ct or mri. These imaging studies are needed to tell if there is a fracture. Most neck injuries are muscle strains.
Xray. The only objective way of knowing if you broke your neck or not, would be to do an xray or ct scan. Unless you see a bone sticking through your skin, you are at the mercy of guess, otherwise.