Is it odd to develop a stutter as a teenager when you never had one before?

Unusual. It is uncommon for a stutter to begin in adolescence. If this has happened it is likely related to increased stress or anxiety.
Yes. This is unusual but not unheard of. You should see your doctor to be sure there are no underlying causes, such as anxiety disorder, panda's or neurological problems. See nimh web site: http://intramural. Nimh. Nih. Gov/pdn/web. Htm.