How can I strengthen my lower back muscles alieviate te pain in my lower back?

I think you are going about this wrong. If you try to strengthen your back right now you are only going to make a stronger back full of pain. The pain in your back is because of pinched or tight muscles. They have to be released before you are going to get any of the relief you are looking for. Once they are released you will be able to go on with life without worrying about what you have to do next, for there isn't anything. The pains are created when we do something wrong or twist or turn and get that muscle pinched or lift something too heavy. Whatever the cause isn't even important, it's understanding that even a strong back can have the same problem and have to do the same thing to release it. Here is how you can get your relief:

Back:

Place your left hand on your left knee. Place your right hand over your left shoulder and with your fingertips find the muscle next to your spine. Press on it and hold. Relax, take a deep breath and exhale and don’t tense up any part of your body. After about 30 seconds there should be a release happening and when it does slowly lower yourself forward onto your right leg. If you can lean over the outside edge of your leg it will be better for your release. Continue holding for a total of one minute. Then release but rest your body there for one minute longer. Then reverse and do the right side.

You should check this Sciatica Natural Treatment

http://cure-sciatica.info/

Normally, I would not answer a question like this as my expertise is generally in medication but I had severe sciatica while I was pregnant with my 3rd child (after having had twins) and I had sciatica so bad that I was finding it difficult to walk. I tried massage therapy and physical therapy and could not take medication

I went to the chiropractor and the pain was instantly relieved. My hips and lower back were out of alignment because I had carried twins the year before. On occasion a Doctor of Osteopathy (DO) can also work but they usually only work on one joint at a time - the chiropractor will do your whole back which works faster. Anyone who does not believe in chiropractors will tell you they are quacks - don't listen.

I don't necessarily believe that chiropractors can cure things like diabetes but they can definitely relieve some types of back pain especially if a pinched nerve is involved which is usually the cause of sciatica. Try a reputable chiropractor ASAP!

Lay on the floor. Lift your legs up by pressing the small of your back to the floor, and don't use any leg muscle to do this. This is a great work-out for the abs and lower back. After that, pick up your shoulders off the ground, and put your hands behind your head. Make a bicycling motion, hitting your alternating elbows to your knees. (Example: Right leg to chest, left elbow touching it.) Do this for several minutes. These are some great, easy, and quick work-outs that give you strong abs and great back muscles! Good luck.