I have the same problem. There's some great yoga videos specifically for stretching the neck and shoulders. Doing those regularly really helps.
I’m much the same at work and I got a sit stand desktop, which are reasonably priced and I stand up once every half hour throughout the day. I also do stretches at my desk once an hour, I just got those stretches on line. Three times a day I do stretches that my physio gave me but you can look in line for stretches to do that are specific to your needs e.g. if you have back problems or neck issues etc.