My 3 month old baby's head locks when turned to the right- what is wrong?

Possibly Torticollis. When a baby will only turn the head to one side, it's often a condition that we call torticollis. It can have a number of different causes, and the key to helping kids is understanding that underlying cause. Whatever the cause, it can be useful to alternate which end of the crib or changing table you place her head. This is a good idea for babies in general.
Position. Often a baby will begin sleeping more on one ear than the other & that can gradually cause a shortening on the neck muscle on that side & even flattening of the side of the skull.The neck will be harder to turn to the opposite side when that happens. Gentle movement of the chin from one shoulder to the other over time can loosen the stiffness. Your doc may need to rx some therapy if it persists.