If you are able to use mods in your game there are some solutions I have found
Using the MCCC mod by Deaderpool, you can click on a a nurse or doctor in the hospital and use a self-command to get them to perform some basic work functions.
You can also use the Keep A Doctor At Hospital mod by LittleMsSam/Scumbumbo in the early part of your medical career so that they can help when you are just an orderly or nurse
The mod Better Hospital Staff by Simvasion allows to patients to be automatically processed into beds and they will get fed. Doctors won't help you with your diagnosis tasks, but they will appear to be checking on patients.
