A clicking sound like that is usually associated either with bones/joints making a self-adjustment (like what a chiropracter does to you, but on its own), or with tendons/ ligaments getting "stuck" briefly as they pass over the bone during motion (mostly associated with the shoulder joint, hip joint and knee joint). Either can occur with or without pain. Since the onset of your pain seems to coincide with your resistance-chair-stretching, I would think the latter would be the most likely explanation. You'll probably need a doctor or PT to determine if it's something that will resolve with time, or something that needs medical intervention.