Sounds like sciatica…i've experienced that and it's very strong, very intense.

i do back exercises such as lying on my back, pulling one leg up to my chest and holding for 5 sec. with 10 reps.
Then, after that, I pull both legs up to my chest and roll to one side, trying to keep my shoulder blade on the bed. I hold for 5 sec., and repeat 10x.
Also get on hands and knees and curl back like a cat and hold. Then drop abdomen and hold. repeat 10 times.

Ice packs might help on the lower back as well.

I've never found regular Tylenol or aspirin to help, but rather NSAIDS to decrease any muscular pressure on the nerve.

if it continues a bit, best call the doc…

Sorry you're hurting so yn