Bryn, your LBS will likely have spare stems for you to try out and would swap to a shorter one at no extra cost. Your body will also adjust as you get used to the new position and you might find you need to swap back to a longer stem after all.
A lot of people swear by getting a professional bike fit and I'm sure they're great but if your flexibility and strength improve so will your ideal position.
As I'm sure you know, the angle of your saddle can also be a factor and if the nose ttilts down for example, you'll be putting more weight on your hands which can be a cause of wrist/hand/thumb pain.
Most of the above is based purely on my own personal experience and from that I'd say what you're going through is pretty normal when getting back into using dropped bars from flats.