How would I know if I have a lower back strain or something more serious?

See doctor. If your pain has persisted for a while would recommend that you see your pcp.
Back Strain. Low back pain is a fact of life. Just about everybody will suffer from it sooner or later. One of the main causes of back pain, whether acute or chronic, is low back strain. http://www.webmd.com/back-pain/guide/low-back-strain.