Does she ever have wetting accidents? That would correlate with both worms and constipation.
But I also second the anxiety thing. I have heard that before too! The lady I jobshare with said when her DD suffered terrible stomach pains (often resulting in hospital visits) they ended up at a child psychologist's office.
The psych said many (often very intelligent) kids think and worry about the same stuff you do, only they don't have the maturity to put things into perspective. She made simple changes (like not watching the news in front of her kid!) and trying not to build up any situations (like when she got the pains instead of quizzing on her on the type, intensity, position etc of the pain, she'd just suggest a lie down or a cuddle and be as soothing as she could.