You’ve gotten several great suggestions from others and, as an avid cyclist, I’d like to offer further insight.
Even with a proper bike fit you can still experience tightness in your arms, shoulders and neck. A lot of this will have to do with your confidence on the bike. The more riding experience you have the more relaxed you will feel on the bike. While riding check your grip on the handlebars. Change hand positions often from placing your hands the top of the handlebars to riding with your hands on the brake hoods to getting down in the drops. This habit can provide relief to your hands and wrists as well as your back and arms. Another thing to check is the width of your handle bars. If your shoulders feel compressed you may need wider handle bars. After being properly fitted to my bike with the handle bar width matching my shoulder width I experienced similar problems that you are. Getting wider bars helped me.
Even with a proper bike fit sitting on a saddle leaning over your handlebars and supporting a 10-12lb. head does place stress on your body with the back, shoulders, neck and arms taking most of it. Strengthening your core and your upper body will pay big dividends alleviating discomfort and adding pleasure to your ride.
Best of luck!