Do you have a death-grip on the bars? Make sure you bend your elbows and relax your hands & fingers completely. You should be able to wiggle all your fingers including the thumb; all at the same time...
I invented an exercise for the delts. I also do other trap exercises, but this is
my favorite for that area. The basic motion is the same as drinking a cup of coffee. Lean froward
and rest a hand on a weight rack so that your back is at a 45% angle. Take a dumbell, palm down, and move it up and down about a foot ending around your nose. You want this to get the delts, so you have to avoid involving the elbow.
If you are doing this right you will get the rear delts, but it also works the front ones. You need to strengthen your shoulders to fix the problem.
Try doing a press exercise like pushups or bench press. Then use you arms as shock absorbers when you hit a bump. Seated rows are also good for cyclists.
My gym has a delt machine that is just terrific. In general, I go to a gym that has day passes, mostly
I go once a week, so that works best for me.
I'm doing something along the lines of what late suggests. I've noticed a sort of "crick" in my upper right shoulder behind the neck area. I've solved it to some extent by doing pushups while on the bike as I'm riding. Just a couple at a time but it's worked out well enough that the crick doesn't bother me.
At home, I try to incorporate pushups in my workout routine.
I dont do much exercises expect swim sometimes. I have never been fitting for my bike. Maybe i should get fitted.
In that case, it's a good place to start. I've had a similar problem when the reach to my bars was too far. If you search this site, there's been plenty of discussion here, and there are plenty of other online bike fit resources out there. Or just go by a bike shop and have someone look at you on the bike.
Another possibility is maybe you're unconciously tensing your shoulder or upper back as you ride, subjecting it to a fairly intense isometric workout. Good luck.