Raising your stem will help. But you will lose some positioning advantages for fast riding downhill. Part of this is conditioning. When you are down in your drops you have to look up more aggressively and this will cause muscle strain if you are a new rider. I don't disagree with using a stem with a higher rise but you could also solve this problem with exercises and focusing on relaxing your shoulders while riding.

I really like the first 5 exercises on this site for this type of problem:

http://ehs.sc.edu/Ergonomics/Exercis...0Exercises.htm

Hope this helps.