Final answer:
The nurse likely suspects the Somogyi effect, where a high dose of insulin at night causes hypoglycemia followed by rebound hyperglycemia in the morning in a child with type 1 diabetes.
Step-by-step explanation:
When a child with type 1 diabetes presents with symptoms of hyperglycemia, diaphoresis, and headaches in the morning, the nurse may suspect the Somogyi effect. The Somogyi effect is a condition where a high dose of insulin induces hypoglycemia during the night, and the body's counter-regulatory hormones then lead to rebound hyperglycemia in the morning. This is in contrast to the dawn phenomenon, which involves morning hyperglycemia without prior hypoglycemia, and is due to the normal circadian rise in hormone levels that increase insulin resistance. Hypoglycemia and hyperinsulinism would not typically cause the hyperglycemia seen in this scenario. Moreover, hyperinsulinism refers to excessive production of insulin, usually due to pancreatic tumors, and would not be expected to cause morning hyperglycemia given its association with hypoglycemia.