Can frequent use of antibiotics hurt a child's stomach or intestines?

Yes and no!: Many antibiotics can cause some GI upset . However, antibiotic colitis is always serious potential problem.

Possibly: Many antibiotics can cause GI upset/nausea/loose bms. Any can even cause an infectious diarrhea caused by clostridium difficile; so limit antibiotic use to when doc prescribes them. Don't demand them for viral illnesses like flu or cold. Follow directions that come with the antibiotics: do not double doses unless told to do so.