If your Trek has one of those padded Bontrager saddles, I would bet money that is at least one of your issues. But too much leaning on your hands and pain between your shoulder blades could also be bike fit... I'm no fitting expert, but you shouldn't have that much discomfort on a 20 minute ride.

I have 2 Treks and even the Bontrager saddle on my Madone was a "gotta go". Pretty white saddle, but no way could I ride on it.