If shoulder distocia happens during childbirth does it mean it will happen again with the next childbirth?

Not necessarily: Shoulder dystocia varies with the size of the baby, the size of the outlet and the elasticity of the pelvis during delivery. Although it may happen again it also may not.

Shoulder dystocia: No: it does not mean automatically it will happen. That said your gyn may elect to do a cesarean if the shoulder dysotica was severe enough.