I'd wait a bit before swapping the stem, at least for a longer one, personally.

Pain between the shoulder blades could easily be from looking up from the "road" position over distances longer than you are used to, and since you aren't used to a road position at all...

I got the exact same pain at about mile 75 of my first century because I was only used to going 50-60 miles. Like you it was gone when I got off the bike.

Raising the stem, if possible, or getting a stem with more rise will help that by sitting you more upright. You don't want to go too far either direction though, and some of it is just getting the feel for a new position, so waiting a few rides and letting your body adjust some might be the better option.