I used to be a bad nail biter. Then, one day, I was really embarrassed at how my hands looked with the raggedy, chewed nails. I started to go for weekly manicures and that did the trick. But that was years ago before this new thing I'm going to suggest.
And, here it is. Go out and, regardless of how short your nails are, get a Gelish or Shellac manicure. This manicure is great because it dries to a hard finish in minutes, so you don't have to sit around the salon waiting for it to dry. When the manicure is over, you can reach right into your pocketbook and pull out your car keys without ruining it! It's so sturdy that it doesn't chip easily and it doesn't peel off. And, it makes your nails feel hard. The polish stays on your nails for about 3 weeks and, once your nails are polished, you might not want to bite them. Go for manicures every 3 weeks and maybe that will work?
When my nails were polished, even when they were short and I'd just do one coat of a super pale pink, I wouldn't want to bite them.