It is not permissible to draw or photograph animate beings such as humans, birds or animals. This has been discussed previously in the answer to question no. 8954.
An exception is made from that in cases of necessity, such as photographs for passports or ID cards, or photographs of criminals and the like.
That also includes what you have mentioned of drawing or photographing the face and whatever deformities or injuries are in it before doing surgery, and keeping the picture in the medical records. This is a case of necessity, in addition to the fact that the picture is incomplete. But in that case it should be limited to a photograph and should not be drawn, because drawing is more haraam than photography; the majority of fuqaha’ are of the view that it is forbidden to draw animate beings, whereas in the case of photography, there is a well-known difference of opinion among contemporary scholars concerning it.
Shaykh Muhammad ibn Ibraaheem Aal al-Shaykh (may Allah have mercy on him) said:
If the picture is incomplete, such as a picture of the face or head or chest, and so on, and something is removed from the picture that represents a part of the body without which there can be no life, then the words of many fuqaha’ indicate that it is permissible, especially if there is a need for that, which is partial depiction. Whatever the case, people should fear Allah as much as they are able to and should avoid that which Allah and His Messenger have forbidden.
“And whosoever fears Allaah and keeps his duty to Him, He will make a way for him to get out (from every difficulty).
3. And He will provide him from (sources) he never could imagine”
End quote from Fataawa al-Shaykh Muhammad ibn Ibraaheem, 1/167.
And Allah knows best.