What you're describing sounds less like early Christian medical texts than it does like a genre of Mesopotamian texts concerned with demons, the diseases they induce, and how to drive them out. This genre of texts includes both generic texts for driving out evil sprits(such as maqlû, an exorcism rite), texts giving instructions for the curing of disease by driving out maleficient demons such as uttuku lemnutu and its forerunner UDUG.HUL, and texts that summarize the symptoms that define various conditions and the associated demon such as the "diagnostic handbook". The literature on these texts is absurdly voluminous and I cannot claim to have mastered it; for two good starting points I recommend JoAnne Scurlock, Diagnoses in Assyrian and Babylonian Medicine and Tzvi Abusch, Corpus of Mesopotamian Witchcraft Rituals, as well as this article on recent-ish developments in the field: http://www.jaas.org/edocs/v19n1/Biggs-Recent%20Advance.pdf