I got my nose pierced a week ago and today I pulled out the stud by accident and it hurt to put it back in.about 30min later my nose got purple-red ish.. is that normal?

It's likely that some irritation and redness will occur when you accidentally pull out a fresh piercing, but irritation that dark and fast sounds like a problem. Clean the area with rubbing alcohol--spritz or pour it over the area, so it can get inside the piercing--this usually helped me when my piercings would get infected. If the discoloration and pain worsen or do not go away, see your doctor ASAP!