Homeric Hymn 16
1] I begin to sing of Asklepios, son of Apollon and healer of sicknesses.
In the Dotian plain fair Koronis, daughter of King Phlegyas, bare him, a great joy to men, a soother of cruel pangs.
 And so hail to you, lord: in my song I make my prayer to thee!
Source: Prayers to the Gods of Hellas
Blog posts about prayers to Healers:
Mostly reblogging of other blogs that have resonated for me although Prayers for Chronic / Acute Illness is kind of a roundup post.