Hi ! I have this problem less often than I used to, but still...

It sure does sound like the sciatic nerve!
You need to lie on your back, pelvic tilt (small of back against flat bed or floor) and use a rope or belt and try stretching your legs (one at a time) up towards your head as far as you can without damaging. It might hurt, like down your leg, but if nothing much more, keep stretching. Do both and often hold for up to 3 minutes a leg (or work up to it) and do this several times a day.

Next, while on your back, draw your knees (again, one at a time) up to your chest and hold it with your arms for as long as you can.

Both the low back muscles and the ham strings need to be stretched to help alleviate this issue.

If you can tolerate ice .. or heat .. now's the time to ice the low back while you're lying down.

What is happening is your muscles are pulling your sacrum out ever so slightly, but it's impinging upon your sciatic nerve. If you can get those muscles to release, allow the sacrum (or ilia ... you've heard of the sacroiliac?) to go back into place. The ice is a good choice for me because with the above, the area swells as a reaction, and causes worse pain. So after stretching (and plenty of times as I can) I numb it with ice.

I've also done "ice massages" ... use a paper or styrofoam cup and freeze it full of water (did I say that right? I 'm really fatigued) Sit on the toilet if you wish and peal the paper back from the ice (never let it drag on your skin!!!!) and move it around the low LOW back.. helping to numb the area. This will also reduce any swelling. You can do this anywhere, but I find allowing the melting ice to drip into the john is easiest. (Plus my toilets are handicap heighth and allows for the sacrum/ilia to go back easier.)