Also remember that your position on the horse can give you aches and pains. If you are sitting even slightly crooked, or maybe have one muscle slightly tense where it shouldn't be, you can get aches and pains like you're describing. Talk to your instructor about your position and where you are getting sore and see if they think the two may be linked.
Once you talk that through and act on it possibly, go and see you dr. Most likely they'll ask for ultrasound to be done, it could be something like bursitis, which is where the fluid lining your tendons becomes inflamed and makes it difficult for the tendons to move smoothly over your bones - hence the pain.
With your shoulder, do you get any pain off the horse, say doing up your bra or lifting your arm straight up to the side? These are classic symptoms of bursitis ;)