What could be the cause of pain inferior to middle third of clavicle?

Muscle pain. Most probably muscle or bone pain, if you continue to have it- time to get checked.
Muscle tightness. Assuming that cardiac reasons are ruled out, the pain you may be experiencing may be muscle tightness at the coracoid process or experiencing costochondritis. You should have this evaluated by your pcp to make sure it's not anything more serious.
Muscle spasm. It could be muscle spasm. There are a couple of small muscles that connect to the inferior aspect of the clavicle. See a physical therapist or athletic trainer, for evaluation.