Classic/Antique Car Repair: 65 Mustang, mustang 289, front end alignment

Question
My 65 mustang,289 engine recently started darting to the left and sometime the right when I drive. I noticed yesterday that there is a thumbnail size groove that has been worn into the inner wall of the front drivers side tire. I don't see any tire rubber on any part near the area on any part that could be causing this groove to be worn into the inner part of the tire. I feel sure this is causing my car to dart to and fro but can't find what is rubbing into the inner wall of the tire. A small bump in the road really causes it to dart, like I lose control for a split second. Things I can grab feel tight under the car.
I though maybe a worn shock but I don;t believe a bad shock would allow for something to protrude into the tire causing this groove. Hope you can help. Tank you.

Answer
This a serious safety condition. You either have a tie rod end that is about to come apart or a defect in a ball joint. The darting is the front end  alignment changing caused by the loose or worn part. The wear is the parts actually rubbing the tire.
Brad