There were three choices to choose from and the sentence that is punctuated correctly is the following:
"Somebody said 'No' to me!" wailed the three-year-old boy in desperate frustration when the scissors were taken from him.
Note:
When a quotation or title is included inside a quotation, the inner quotation marks should be changed to single marks. Confusing but read the sentence over and over again to understand and see the difference.