8122,
What do you mean by a "cork stud?" I have never heard that term before.
Are you having problems getting the new jewelry in at all? Or does it go into the outside hole on the nose, but get stuck going all the way through?
If your new jewelry is thicker than the old, the piercing may be too tight to fit the new jewelry. If you had a ring and are going to a stud, or vice versa, sometimes the channel in the nose has healed into the shape of the original jewelry and is a bit inflexible. Relax, make sure the jewelry is lubed up a bit (a dab of antibiotic ointment works fine) and try and follow the channel as you insert the new jewelry.
Remember, lots of fussing can irritate the piercing and cause swelling, which compounds the problem. If you really get stuck, you may have to put back in the original jewelry and go to a piercing shop for some help. Many will change jewelry out for you, but beware that most who do will charge you a small fee for the service if it is jewelry you have not just bought from them.