I apologize if some of this is basic to you. I don't know your level of experience.
Gregg66's remarks ring true. If you are new to the road bike, and particularly if you trust your initial fitting, you should give it a little more time. Some avid road cyclists work through minor stiffness and aches at the beginning of every season. It would be that much more pronounced for you if you're new to it. It gets better. In the mean while, you might be able to do a couple of things on and off the bike to help.
First off - work on relaxing those neck muscles while you ride. This might be just a tensing up issue rather than a strain issue, especially if you're new to the bike. Just try to be aware of tenseness.
Check you posture on the bike - if your torso is hunched over with a lot curve to you spine, try strightening your back a bit. This will roll your shoulders up and to the rear and may provide some relief at the shoulders and neck. However, note that this may also rotate you pelvis down and to the front, which might affect your shadowy parts and/or your back. You have to find a balance.
Check your arms - if they're locked out, you might be in a permanent "shrug" at the shoulders, which will add to the tensing up thing. Your arms should be bent at the elbows slightly, and your shoulders should be in a slightly rounded relaxed position. It helps to loosen up the hands so that your grip is light rather than tight. Really, it's about finding as relaxed a state on the bike as possible. Tensing up creates aches and stiffness, and robs power and energy.
This might sound funny, but check your jaw. Clinching is a sign of tension in the neck and head.
Off the bike you can work on stretching and relaxing those muscles with neck rotations and rolls.
Hope this helps. Good luck.