Her own doctor would be the one to assess her for any regular medical conditions and any stress-based conditions.
The other doctor(s) that could help are those who could ease her worries about you, both your own therapist(s) because they would help you get better, and she would see that and feel less worried about you, and possibly a therapist for her so she can talk about her worries about you.
If the main issue you are concerned about is her appearance, such as dark circles and aged skin, you could also take her to a dermatologist and see if the derm could give her some advice about her skin. A lot of people at 60 look older than they are because of smoking or sun exposure. You can't do a lot to change sun damage besides take care of what is remaining, and I guess there is plastic surgery but I'll bet she wouldn't be up for that. But if smoking has played a role, for a lot of reasons she should try to quit smoking. Her regular doc should be able to steer her to a smoking-cessation program. I will note, though, if she smokes to deal with the stress of your suicidal episodes, she probably won't quit unless you stop being suicidal.