What would cause left side bottom part of rib cage push out about an inch alomg with pain?

Hmm??? Without knowing your history, nor examining you it is difficult to say. Visit your doctor to get a full examination and figure it out.
Pectus excavatum. It is usuallay a congenital condition that if very mild can go undetected. It is hurtfful but not harmful unless it severe. Warning signs are shortness of breath, chest pain (not rib pain), exercise endurance problems, racing heart or other related concerns. It coulg also be caused by a previous rib fracture that healed incorrectly, hurtful, not harmful.
Possibilities. Muscular injury, rib fracture or a hematoma (blood bruise) are all possibilities. A history of fall or trauma puts all of these as strong contenders. An x-ray of the chest would be helpful.