thanks for asking.
You have not mentioned your age. Biting nails and inanimate objects might be an indication of insecurity problem. Chewing something for example chewing gum as the cricketers do may decrease the tension for the time being. But eating your own skin from peeling of feet & hands needs attention.
I suggest you
1. Please do regular Physical exercise.
2. Engage yourself with some hobbies of your choice like Stamp collection etc.,
3. Divert your mind with some regular badminton or table tennis and other destressing activities
like 20 minutes of Pranayama or yoga
If symptoms persist, please have a Psychiatrist