Kenneth G. Wilson (1923). The Columbia Guide to Standard American English. 1993.
sick to (at, in) the stomach
These are American regional dialectal variants of the same locution; all mean to be nauseated or to throw up. For example, most New Englanders say sick to my stomach, but most Midwesterners from the Great Lakes region say sick at my stomach. Each locution is Standard in its own region, but outside it will sound odd at all levels.