We get early well-articulated notice of Luke's medical language from M.F. Sadler, The Gospel Acc. to St. Luke, (1890, NY): Introduction:
" MEDICAL LANGUAGE OF ST. LUKE.
'I have given in an excursus at the conclusion of my notes on the Acts of the Apostles some instances of the use of medical language by St. Luke. This subject seems exhausted in a treatise by the Rev. W. K. Hobart, of Trinity College, Dublin, "The Medical Language of St. Luke." He seems to prove very clearly, not only that St. Luke uses medical terms in describing the miracles of healing, which the other Evangelists do not use, but that his vocabulary is that of one who had received a medical education and studied medical treatises; and when writing respecting non-medical matters he yet uses very many words which Hippocrates, Galen, Dioscorides, and other Greek physicians were in the habit of employing even when not writing on diseases and their remedies. To give Dr. Hobart's own words,
"There is a class of words running through the third Gospel, and the Acts of the Apostles, and for the most part peculiar to these books of the New Testament writings, with which a medical man must have been familiar, as they formed part of the ordinary phraseology of Greek medical language. In thus using words to which he had become habituated through professional training, St. Luke would not be singular, for the Greek medical writers, also, when dealing with unprofessional subjects, show a leaning to the use of words to which they were accustomed in their professional language."
I wish I could now give instances. ...So that a searching examination of St. Luke's phraseology yields a striking confirmation to the truth of the words of the Apostle, which describe him as a physician.'To find detailed description of this language, however, we will have to turn to such above mentioned published works. Hobart's book is out of copyright, but is online at Archive.Org.
Preface: "...In order to bring the work withing reasonable bounds, It was found necessary that the number of examples of the medical use of a word should not, in any case, exceed ten; in many instances they could be cited indefinitely. ...An asterisk has been prefixed to those words which are peculiar to the Third Gospel and the Acts of the Apostles, and also to a few words, which, though not peculiar to these writings, are used in them alone of the NT in a medical sense."
(1) Luke 4:23 Ιατρε, θεραπευσον σεαυτον (cf. Galen Comm. vi. (xvii. B. 151)
(2) Healing of Demoniac Luke 4:35 *ριψαν, μηδεν βλαψαν αυτον (cf. Hippocrates, Epid. 1160)
Consulting the Table of Contents allows for a quick listing of important cases. Citations in non-Biblical medical works are found in the main text.