There is indeed. Here is a short but powerful prayer (paraphrasing the prayer that was offered before bloodletting in Talmudic times) that you should say before undergoing a medical procedure or taking medicine:

יהי רצון שיהיה לרפואה

"May it be Your will that this will bring healing."

The words should be said out loud and with clean hands—just the same as saying any other blessing or prayer.

This brings into focus the faith that all healing comes from G‑d; the medicine is only His agent through which He heals us.

Jewish custom is to recite psalms at times of need such as these and to ask others to recite them as well. There are varying customs as to which ones are best to say, but all agree that chapter 20 and 23 are good in all situations.

Charity also provides protection from illness—by giving others life, you yourself are granted life.

In addition, the Rebbe would advise people in need of a recovery to have a competent scribe inspect their mezuzahs (and tefillin) to ensure that the letters are intact and that they are properly positioned.

May you indeed be granted a full and speedy recovery!

Rabbi Menachem Posner

Note:
There are various (somewhat longer) versions of this prayer. The above text was recorded by the Rebbe in Reshimot, volume 8, page 236.