My neck back and chest muscles are so tight that I pull those muscles just sitting at my desk somehow. What are some good stretches to prevent this?

Need expert instruc. This sounds like a muscular problem make an appointment with a physiotherapist. I'm sure your family doctor can recommend someone for you.
Check out these. Links. Taking tylenol (acetaminophen) or nsaids (motrin or aleve ) should help.Hope u feel better soon! http://www.active.com/mind-and-body-yoga/articles/4-simple-yoga-exercises-for-back-and-neck-pain?stop_mobi=yes. http://m.youtube.com/watch?v=cty-phttit0. http://www.active.com/tennis/articles/5-tips-to-end-neck-and-back-pain.
My own experience. Try some heating pad on the neck, then do some exercise on the shoulder blade muscles- a few sessions with a trainer may be worthwhile to improve your posture. Try to get up for a few minutes and stretch for every hr you spend at the desk. I am sure there will be many more suggestions from others in this panel.