Get your neck checked. Pronto. There could be impingement on a nerve, blood vessels or the vertebrae themselves may be damaged. Some folks are born with minor cervical neck issues that go unnoticed until they get into odd positions -- and a drop bar road bike is among the oddest of the odd.
My C1 and C2 were cracked when my compact car was t-boned by a full size SUV at 50+mph in 2001. Both are permanently damaged now and I can feel it worsening over time. Even after years of physical therapy (it's a daily thing now) I'm still very position-sensitive on a bike. A fraction off in bike fit and rough roads can cause blurry vision from nerve issues in the neck. So I adjust my bike fit as needed to suit myself.
And in my early 60s I'm comparatively fortunate. On a ride a couple of years ago I met a fellow riding cross country who wore a neck brace. He was a paramedic or EMT who was struck by a drunk driver on an emergency medical stop. Nearly paralyzed, laid up for a year. When he finally got out he wanted to ride a bike cross country before his neck worsened. He's only in his 30s. During the 10 or so miles we rode together he had to get off an walk once or twice just to give his neck a rest and different position. He was damned determined to ride across the US in that condition.
One reason I really like my old school steel road bike with quill stem is it's easy to adjust an 1/8" or 1/4" as needed to suit my neck, during a break in long ride. With my two carbon bikes with threadless I'm pretty much locked in unless I want to tote a mini torque wrench and spacers (which I have done to make adjustments on longer rides when shaking out my fit on both bikes).
And if you do have neck problems do not EVER allow a chiropractor to make "adjustments." Discuss everything thoroughly up front. Gentle constant traction may be okay. My favorite physical therapy wizard has the magic hands for that. But I won't allow any chiropractor to do neck adjustments. One wrong move and I'm paralyzed or dead.