I had a bad back a couple of years ago...not as bad as yours by the sound of it, no spasms thank goodness.
I saw a physio (NHS so no charge) who gave me exercises that worked very well.
He also suggested that the issue was postural from sitting at a computer. I only had a desktop at the time.
The computer posture suggestion was bang on the money as, if I sit at the desk top now for any length of time, my bad back returns.
So....my suggestion to you is to see your GP, get a physio referral, but most of all check your posture whilst at your computer.
Have a look at a skeleton and try to ensure that your back is curved the right way, kind of like a reversed S shape.