Definitely! Prayer for their well-being would be a great act of lovingkindness in addition to the mitzvah you fulfill in your more “conventional” medical efforts.
There is a beautiful prayer that is purported to have been composed by Maimonides who was himself a doctor. It reads:
O God, You have formed the body of man with infinite goodness; You have united in him innumerable forces incessantly at work like so many instruments so as to preserve in its entirety this beautiful house containing his immortal soul, and these forces act with all the order, concord, and harmony imaginable. But if weakness or violent passion disturb this harmony, these forces act against one another and the body returns to the dust whence it came. You send then to man Your messengers, the diseases which announce the approach of danger, and bid him prepare to overcome them. The Eternal Providence has appointed me to watch over the life and health of Your creatures. May the love of my art actuate me at all times, may neither avarice, or miserliness, nor the thirst for glory or a great reputation engage my mind; for, enemies of truth and philanthropy, they could easily deceive me and make me forgetful of my lofty aim of doing good to Your children. Endow me with strength of heart and mind, so that both may be ready to serve the rich and the poor, the good and the wicked, friend and enemy, and that I may never see in the patient anything else but a fellow creature in pain.
If physicians more learned than I wish to counsel me, inspire me with confidence in and obedience toward the recognition of them, for the study of the science is great. It is not given to one alone to see all that others see. May I be moderate in everything except in the knowledge of this science; so far as it is concerned, may I be insatiable; grant me the strength and opportunity always to correct what I have acquired, always to extend its domain; for knowledge is boundless and the spirit of man can also extend infinitely, daily to enrich itself with new acquirements. Today he can discover his errors of yesterday, and tomorrow he may obtain new light on what he thinks himself sure of today.
God, You have appointed me to watch over the life and death of Your creatures: here I am, ready for my vocation.