One thing you can try is to always carry a small nail clipper in your purse. May seem icky, but if you get the urge to bite (or if the skin catches on something), try clipping instead of biting.
You may end up with one obsession in place of the first one (plus a lot of people don't like to see this kind of grooming in public, so pick your moments), but it will be a lot cleaner and you'll be less likely to get infections. Plus, if you need to pick your moments or go someplace private in order to do this (e. g. a bathroom stall or the like), you may find some of the habit being broken because of the delays.
If you can't instantly gratify an obsessive habit, that does help to break you of it. At least that's been my experience.