A bike fittting would definitely help rule out length of top tube, stem, etc. But you also are now bent over in a more aero potion requiring more back and neck strength. Is this pain immediate or does it appear later in the your rides? Tired riders will sometimes let their shoulders and back kind of cave in between their shoulder blades. Upper body strength can help.

Also, you now have more hand positions and should be changing your position frequently. This will help with hand pain even if the bike doesn't fit quite right. Do you have any experienced roadie friends who can help with bike fit until you have the money for a professional fitting?