I've been having really bad low back pain recently with sharp pain down back of left leg, specifically when bending over, lifting, or coughing. ?

See a doctor: This could be a disc herniation in the back. This could cause the symptoms that you are describing. Luckily, if it is a disc herniation, surgery may not be necessary but i would suggest you get this checked out.

Siatica: That's a classic description of siatica most common cause herniated intervertebral disc see primary or wait if the pain is not severe and livable.

Many Possibilities: Depending on how long it's been going on, i would consider an evaluation by a pain/spine specialist. Sometimes it could be a muscle imbalance, early onset arthritis or scoliosis. Also could be a pinched nerve/herniated disc. Either way it might be good to figure it out and get appropriate treatment.

This is most : consistent with a disc source of nerve compression or irritation although there can be other possibilities. The fact that you can increase the pain with bending & lifting & worsen the pain with coughing most likely to find a disc problem like a herniation or tear of the outer portion of the disc known as an annular tear. These can be treated non operatively 90% of the time. Start with your doctor