What could it mean when you have a sharp, throbbing pain in your lower left leg?

Leg pain: It could be multiple things and some of them are urgent. For one sided leg pain, one must consider: neurological issues (nerve entrapment, nerve irritation, nerve compression), vascular issues , blood clot or dvt, metabolic issues, and musculoskeletal issues like a strain, fracture... It is best to see your doctor to rule out any serious problems.

Irritated Muscle: Generally a muscle spasm is an irritation of that muscle. Sometimes this results in an abnormal continuation of muscle tension that results in pain longer than expected. Muscle spasms have a reason, its your body's way of telling you not to do what you just did.