Will my big toenail grow back from being pulled off?

I was wearing a new pair of shoes to work and after I got home, my feet became very sore. So because of this, about 2 weeks later my toenail began to detach itself from the nail bed. I got so frustrated from the feeling of it being loose, that I pulled it off myself using a pair of nippers. I'm afraid I damaged the cuticle or root that it may not grow back. Also, how can I treat this toe? Should I apply some Peroxide, Neosporin and/or tea tree oil to the nail bed?