I'm sorry you are experiencing that pain - I know it is pretty unbearable. I have had bouts with sciatica and these exercises helped me. Over the past few years, I've consistently exercised, done weight training and stretching and as my core muscles developed, my back pain disappeared. Knock wood; I haven't had a flare up in a few years.
One other suggestion - if your insurance won't cover physical therapy, but will cover a doctor visit, ask the doctor to give you a list of exercises. (somes they will even show you how to do them)
I think it is helpful to walk around some to loosen muscles and to use a heating pad for a few minutes prior to exercise and when done, to ice the area (heat soothes and brings blood to the area; ice will prevent imflamation after the physical therapy)
These exercises helped me to stretch my lower back and strengthen my core. When I had flare ups, I couldn't do all of them - let pain tell you what not to do. For me it was important to continue to do them when the pain was gone so I could prevent more problems. I don't know how my descriptions will work - I find I prefer to see it done rather than read a description and I'm certainly not sure I am clear, lol. You may want to check out You tube for some videos to see exercises
Lie on the floor, bend both knees and pull your legs in towards your chest to stretch out those muscles.
Lie on the floor knees bent, cross left leg over right and gently push the leg toward the floor on the left...Change legs and do it to the right (don't push this...just go til it feels okay)
Cat stretch: Get down on the floor on your hands and knees. Push your back up towards the ceiling like a cat arching it's back -feel a gentle stretch in your back Hold for 10-15 seconds then return to start
Pelvic Tilt: Lie on your back with knees bent and feet flat on the floor
Exhale and press the small of your back against the floor and hold for a few seconds. Release.
Crunches help with ab strength - It's important though not to do it in a way that you pull on your back or neck or jerk to try to lift. I lie on my back, lift both legs straight about 60degrees, then lift my arms straight and try to make my body like a v...hold for a couple of seconds then back down.
Also for core - lie on back, lift both legs (straight) to about 60-70 degrees and slowly lower almost to the floor. Don't let them touch the floor...when it gets close, bend your knees, lift the legs back up, straighten, and slowly lower again. (you can do like a scissor kick as your lowering too if you want)
Lie on the floor, bend your right leg with right foot flat on floor; raise your left leg in the air (straight up) to 90 degrees and wrap your arms around the back (above knee) and gently stretch...Switch legs. Helps stretch the hamstrings.
If you can do it (when pain subsizeds) lie on stomach, arms above head (elbows near ears) and gently lift legs and arms and chest up off the ground, hold and slowly lower.
Get on all fours, and s lowly extend your left leg straight behind you.
Make sure that your back remains straight Hold for a few seconds, then return to start and repeat with other leg. Once you get stronger, you can lift the opposite arm at the same time and hold.
Hope this gives you enough variety to pick some that work for you without too much pain and sure hope you feel better soon!