It sounds a bit odd, but go to somewhere like Staples or PC World , somewhere that sells those black leather 'managers chairs'
http://www.pcworld.co...air-03109985-pdt.html
Try sitting in them in the shop, and you will find them surprisingly comfortable.
Get yourself one that has really good support in the lumbar region (behind your lower back), and after a while sitting properly you may find your problem improves.
The worst thing I can do for my back is slouch on a settee.
If you want to experience a really good chair for your back, go and see what a quality retirement home provides for their elderly residents.