The contraindication for administering a measles, mumps, and rubella (MMR) immunization to a child is a history of hypersensitivity to gelatin.
1. **History of hypersensitivity to eggs:** This is not a contraindication for the MMR immunization as the vaccine does not contain eggs.
2. **History of anaphylactic reaction to bee stings:** This is not a contraindication for the MMR immunization since bee venom and the components of the vaccine are different.
3. **History of anaphylactic reaction to gelatin:** This is a contraindication for administering the MMR vaccine as gelatin is a component of the vaccine and can trigger an allergic reaction in individuals with a known sensitivity to it.
4. **History of hypersensitivity to shellfish:** This is not a contraindication for the MMR immunization as shellfish is not a component of the vaccine.
Therefore, the presence of a history of hypersensitivity to gelatin would prevent the nurse from administering the MMR immunization to the child.