A Question About Dog Nails?

Okay so i was taking my puppy for a walk two days ago and we were crossing the streat in the cross walk when two cars sped around the corner. I had no time to pick my puppy up so we just took off running trying to get out of there way but they turned on there brights and it scared the crap out of my puppy. he floped to the floor and clung his nails in the ground. There was no way i could pick him up in time or we both would of got hit by the car. So I pulled really hard on his leash and drug him to me. When he got close enough i grabbed him and we fell onto the sidewalk. I got some scraps but the bottom of his paws got hurt. His pads got kind of like a bad rug burn on them. I cleaned and disinfected them pretty good. I stoped the bleeding but it looked like one got burned pretty bad. I wd it up but he just tore the gauze off. It wasnt bleeding so i didn't put the gauze back on. I've been cleaning and disinfecting the burns since then but today i noticed blood on my arm when i was holding him. It looks like he has been licking the paw that got really bad rug burn so much that the skin is raw and a little of it has come off and now it looks like the nail is coming out. My question is if his nail fully comes out how long will it take for it to grow back?