Start with bog standard (but the short length, as you'll struggle with longer) press on nails fixed with sticky pads. They'll cover up your nails and make it harder to bite at the skin. Yes, you'll need to keep on replacing them every 3 days or so, but that's partly because they're just sticky pads and partly because your nails are so short.
As you keep on doing that, your nails will have a chance to start growing and the skin start to heal.
Through the next few weeks, when you change them over (as that'll be one of the good things about them, the ability to have a complete change whenever you feel like it with no damage), take the time to give your hands a good clean, soak and gently push any skin that's attached to the nail - that's the cuticle, not the skin on your finger that goes raggedy - back. Don't cut, pull or expect perfection, just push them gently. follow up with a good moisturiser and then before you put on the next set, wash your hands properly again.
It's going to take time - eventually you'll become aware of the feeling that your nails are longer/you can feel them against the nailbed where there used to be nothing. Keep up the cleaning and moisturising, but do not let them go past the tips of your fingers yet; they're not strong enough until the entire nail from base to tip has never been bitten/lifted away from the nail bed.
You may find that you're actually happiest with natural nails exactly at the tips of your fingers, rather than then risking all that hard work to have stuff put on top of them, or you like to have them slightly longer so you can have something else on them. But getting the natural nails healthy and to that length is the key - and you'll be so proud when you do.
ETA: Psoriasis affecting the nails and ex biter. This worked for me.