The direct answer to your question is that yes, this is likely due to a pinched nerve, although it may not be the primary issue, and a pinched nerve can usually be fixed, but it is really more complex than simple answers.
There are several possible causes of the pain that you describe. Pain that starts after lifting could be related to an injury to the muscles, such as a muscle strain, or to the underlying bony structures that support the muscles. The fact that the pain is radiating to the extremities,including the horrific pain in the legs, suggest that there is a pinched nerve,but does not specify the underlying cause of the pinched nerve. It is possible that there is muscle spasm associated with a muscle strain that is pinching the nerve as it travels through the muscle layer from the spine to the legs. It is also possible that there is some degenerative changes in the spine that is pinching on a nerve, such as a herniated disc.
If the pinched nerve is because of muscle strain and spasm,it will usually be able to be fixed with conservative care, such as medicines and physical therapy. If there is an underlying degenerative changes in the spine, it also may respond to conservative measures, but it also may help to perform injections into the spine, and some people need surgery to relieve the pressure on a pinched nerve.
We usually do not rush to consider more invasive treatments,uncles there is evidence of significant dysfunction of a nerve on neurologic exam. If there is significant nerve dysfunction, then it is more urgent to relieve pressure on the nerve. But in most patients, there is not significant nerve dysfunction, so conservative treatment is usually done first.
If I can provide any additional information, please let me know.