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That is a pretty generalized question, being as all three of Newton's laws apply here.
First law states that an object at rest or constant velocity remains until an outside force acts upon it.
Second law states that the force of an object is directly proportional to the product of its mass * acceleration, the famous F=ma.
Third law states that for every action there is an equal and opposite reaction.
So, it is easy to explain that all three laws are in play here because her body (at rest immediately before shot is fired, example of first law) has a force exerted by the mass*acceleration of the bullet (being propelled away from her by the gunpowder, felt as recoil; example of second law) which was returned by her own body on the gun (why she didnt fall over, example of third law). It was her own body making contact with the gun as it pushed against her which injured her shoulder.
Culprits are mostly second and third laws here. Majority of pain comes from the second law, as force=mass*acceleration and the force is what caused the injury but also in part due to the fact she resisted the recoil of the shot.