Is it true that if you injure your left shoulder, your right shoulder will get naturally weaker? i dislocated my right after injuring the left

Not true: You non-injured shoulder may become more inflammed or irritated as you may have to use it more to compensate for your injured shoulder.

Not necessarily: Without knowing the circumstances of your right and left shoulder injuries it is difficult conclude that you injured your left shoulder because of the right shoulder injury but certainly, patients with greater laxity systemically are at increased risk for shoulder dislocation and instability.