So, I am going to scare you with my personal experience.
In 2017 I have what you are describing. Jolts of pain down my right leg that came and went. I talked to my doctor about it and was in the process of getting some physical therapy for it, but it was taking forever to get in.
I did a stupid. I had a work trip. Had to take my personal car as the company one for this kind of trip was tied up. It involved an 8 hour drive in my Miata. I am 6'2" and locally was fine in it, but would get sore after awhile. I get where I am spending the night and go to bed. The next morning I was in pretty intense pain and physically COULD NOT bend over to pick something up off the floor. I struggle through the rest of my trip in pretty bad pain, including the drive home. By the time I got home I had to call my wife from the driveway as I needed help to get out of the car.
Rapid doctors visits, specialist, MRI's... I ruptured the disc at L5-S1 in my back and it was pressing on the nerve. Specialist indicated that I needed a Microdiscectomy to remove the material that was expelled when it ruptured. I was pretty much bedridden, it hurt to get up to go to the bathroom and REALLY hurt to get in a car to go to a doctors appointment. As an aside the same week I was told I needed surgery, my wife and I found out we were pregnant with our first child.
Had the surgery in early December, was pretty much bedridden for 4 months and even after that it was a LONG hard recovery road. I have had epidural cortisone shots a few times and finally, 5 years after the injury, got to a point where it isnt hurting every day and only comes up when I get dehydrated or do dumb things. I wont be going to a trampoline park or anything like that any time soon. GOOD PT was what finally got me through recovery.
The root cause of mine was a long commute and a desk job leading to a loss of core strength and bad posture. The pain I went through was comparable to a kidney stone, maybe hurt a bit less, but lasted a lot longer.
So, my STRONG ADVICE is this. GET YOUR ASS IN TO A DOCTOR AND GET IN PHYSICAL THERAPY - LIKE YESTERDAY! This isnt something to ignore. The "lightning bolt radiating pain" is nerve pain. Engauge with a good therapist and start working in a good core stretching and strengthening regimen with their guidance. An ounce of prevention will save you A WORLD OF PAIN.
And whatever you do, dont do something absolutely stupid like an 8 hour drive in a car you know makes you sore. It wont end well, trust me.
As SKJSS says, orthapedic is where you are headed. Internet diagnoses arent worth squat, but bulging disc is a likely culpret and bulging leads to rupture if you arent careful.