Make your bars and hoods look like those in the attachment. Minus the bit of white bar tape under the hoods and the dirt and torn bar tape, and don't even look at the rest of Fred.
But make the bar tops and hoods all in one plane like this. Then ride with your hands on the hoods almost all the time. Look at photos of pros. Bar tops when climbing is good, hands in the drops only when pulling a paceline, riding hard upwind, sprinting, or trying to see how long you can hold 30 mph. If you are already doing all of this, try neck stretches and rolls. Normally one sees neck pain in those who are increasing their weekly mileage too quickly. And normally it goes away with a bit of rest and then a return to biking. And if it doesn't fit these "normal" standards, doctor or PT.