Has the old one deployed then? splitting the seat cover?
One thing, you cant just fit a new air bag and then stitch up the cover on mothers sewing machine, the stitching has to be done in a proper way so it will deploy properly next time the air bag is needed.
Workshop manual tells you how to replace all the airbags except the ones in the seat unfortunately, but you will obviously have to pull off the seat back cover to get at it and then get that repaired too or replaced with an undamaged cover.
I think I would get the cover off and have a look, its no good as it is anyway.