One of my favorite sayings is that non of my patients ever read a medical textbook. By that I mean, doctors don't always know what they think they know. In medicine, there is an exception to every rule, and rarities do exist.
Since the itching seems to coincide with her heat cycles, spaying her will prevent future heat cycles and if the hormone changes that occur at that time are truly the cause of her itching, then spaying her should be the cure.
Certainly, spaying will not aggravate any other cause of her itching.
Be prepared though, that it may just have been coincidental with the onset of itching and her heats (although, l have to agree with you that two times could make one draw the same conclusion as you).
Spay her then wait and see would be my best recommendation.
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No doctor patient relationship is formed by this communication. This advice is no substitute for a complete physical examination and appropriate diagnostics provided by a licensed veterinarian.