Have you tried Physical Therapy yet? That's what's worked for me in the past (and pretty much everyone else I've known who's sprained back muscles). Try the PT. If it is too intolerable, see if there is anywhere around you where you can do aqua therapy, where you do the exercises in a heated pool. It will take time to heal, though, even with the exercises. Best thing to do is avoid further injury & work on gently restrengthening the muscle(s) that was injured.
Also, you could try putting warm washcloths or a heating pad on the area that hurts. It prob. won't get you better any quicker, but might lessen the pain in the meanwhile.
Best of luck to you! Hope you start feeling better soon!