I've heard about levofloxacin cause tendon rupture. does levofloxacin cause stomach damage?

Yes and no: Not in anywhere near the same mechanism as with tendons, but all antibiotics can potentially cause some degree of stomach and GI problems by killing the normal bacteria that populate the GI tract. This can cause thrush in the mouth and diarrhea in the GI tract by over growth of pathological bacteria. Don't hesitate to be seen if you are having problems.