Sounds like Sciatica! A question do you keep anything in your left back pants pocket?
like a wallet! If you do then don't! If it's Sciatica it will help not keeping anything in your back pocket as that will cause pressure on the nerve.
I have had the exact same pain but in the right side, it may help you to read my posts and answers as it explains it all.
I have finally found out after 9 months of suffering that I have torn my hamstring and some bone from where it attaches to my Ischiopubic Ramus bone in my pelvis.
In the process of looking for answers the other possibilities that I ruled out that may apply to you however are: Ischial Tuberosity Syndrome or Ischial Tuberosity Bursitis, Hamstring Tendonopothy, Sciatica as gymdandee suggested, a bulging disc in your back, an inflamed/stuck sacroiliac joint, a stress fracture of your pelvis....
I would suggest you get an ultrasound done looking for Iscial Tuberosity syndrome or Ischial Bursitis as this covers the are where you are experiencing the pain and should show what ever the problem is. Ischial bursitis is little spurs that develop on that part of your Iscium which is part of your pelvis, and is very painful when sitting, and refers pain down your leg and into your butt.
Your symptoms define irritation or compression of the sciatic nerve.
You require an MRI of the lumbar spine and a referral to a physical rehab therapist who will show you specific exercises that will prove helpful. This will be the best money you every spent. They will demonstrate an exercise and watch you duplicate what they do.
Eventually, there is a surgical option to be considered.
In the meantime, avoid lifting and sit on an inflatable cushion when riding in a vehicle without good suspension.