You can apply for worker's comp, but will most likely not get it: "sitting" is a not a work-related injury, because sitting is a common life activity that we all do every day and had nothing to do with work. It is very unlikely that a herniated disk from sitting would be considered a compensible work-related injury, any more than if you had herniated yourself while cought at work would be considered something you could get compensation for. That's not to say that you should not try and apply--but don't be surprised if you are denied.