Can a male doctor look at and touch a female patient?

If a female doctor is not available, then this is permissible in case of compulsion. Allamah

Maulana Mufti Muhammad Amjad ‘Ali Azami says:

One scenario in which it may be necessary for a man to look at a non-Ma ram woman is illness. He may need to see certain bodyparts of an ill woman for treatment, in fact, he may need to touch her e.g. touching her hand to check her pulse or touching her abdominal area if there is a doubt of internal swelling, or looking at an abscess are permissible in such situations. He is allowed to look at the affected area, and if necessary, touch the area but only as much as is needed. This is permissible only when a female doctor is unavailable to perform the medical treatment; otherwise, women should be taught methods of medical treatment so that they may  work in such circumstances, because their looking at other women is not as bad as is the looking or touching of men.

Midwives are available in most areas to check any abdominal swelling. If midwives are available then there is no need for a man to check. Even in cases where a male doctor is allowed to look at a woman, it is essential that only the required part of the body is exposed and

the rest of the body must remain concealed so that he cannot see it.

(Ibid, pp. 90-91)

If merely ‘looking’ is necessary, then touching is not permissible by Shari’ah. Remember! Touching is worse than looking.