My left palm by my pinky started hurting. Why?

See an orthopedist. You should have it evaluated to rule out nerve entrapment problems involving the ulnar nerve in guyons canal, ligament or tendon inflammation/strains/tears or even subtle fractures. Basic treatment consists of resting, use of a over the counter wrist splint, avoidance of painful activities, icing especially if re- irritated by ongoing activity, and use of anti-inflammatories.