I had the same problem when I started playing. I played without nails for a year.
What I did was I went to a nail salon and got acrillic nails just on my right hand. I did feel weird going in but the lady who did my nails said that a lot of guitarists come in. And it only took like 10 minutes.
The nails fall off after a month or two and underneath you have fresh grown nails. I found that since they were already long, I had no integrity to bite them off. My left hand I still bite.