While perhaps a bit small, the frame is probably close enough to be adjusted for you. Unfortunately it's really hard to say for sure, especially with a medical condition involved. There's always going to be some discomfort in riding a road bike long distances. It also takes time for your body to adapt to the position and build up the core strength to hold a forward position. An upright riding position is not the universal answer for back pain that some people make it out to be. Some riders find that putting so much weight to the rear transmits vibrations right up the spine while a forward position relieves it. Exercises to strengthen your abdominal muscles would certainly help. Since you do have a medical condition a session with a good fitter would be a help.
__________________
Telemachus has, indeed, sneezed.