There are enough things (between the bike and you) that can cause pain between the shoulderblades, that it would really be a good idea to have a second pair of eyes handy to look at you on your bike and help you problem-solve.
So, if you grab a friend and a copy of Andy Pruitt's Complete Medical Guide for Cyclists you can get a darn good start at figuring out how your basic fit is going. It's a lot of fun to see how it all goes together!
If that doesn't solve it, find a good fitter and pay them a visit. (expect to be charged $150-$200 or so for a fit)
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson