My NT daughter is the one prone to anxiety in our family, and she also is the one with near constant tummy aches, headaches, etc. There is probably a connection, I agree with that statement.
Don't skip over the possibility of food sensitivities, however. I think those play in with my daughter as well, although we haven't pinpointed which foods yet. A sensitivity is different from an allergy, in that the reactions are more subtle, but it is a difficult issue to get a handle on and there aren't yet solid enough protocols for mainstream medicine to be jumping on the concept (some good less mainstream doctors, however - and some quacks, so you have to be careful).
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).