Many parents express concern about the risks of anesthesia for their children. Risk is actually quite low when using anesthesia during surgery. Monitoring is more sophisticated than in the past and anesthesiologists are more experienced.
Given today’s safety standards, the life-threatening risks are very, very low. Your child may experience some side effects, which are generally mild, such as being disoriented, agitated or nauseous. Vomiting, drowsiness, dizziness and a sore throat are also pretty common. Most side effects either wear off or are treatable. I’d opt for local anesthesia whenever possible, as it’s the most mild, but it’s often not practical for even minor surgeries on children.
From The Smart Parent's Guide: Getting Your Kids Through Checkups, Illnesses, and Accidents by Jennifer Trachtenberg.

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Important: This content reflects information from various individuals and organizations and may offer alternative or opposing points of view. It should not be used for medical advice, diagnosis or treatment. As always, you should consult with your healthcare provider about your specific health needs.