Yes that makes sense.
It may take some pressure off you if you can seek support from someone at work, especially your manager, or someone in the hospital staff suppory system, if thete is one, then, at leadt it will be documented, if your work suffers. I work for NHS, in uk, and there is a confidential service for staff.
I undetstand you don'want to jeapardise your job, but depression is so common in caring professions.
I don't know your work set up, but may be worth finding support. You may be pleasantly surprised.
Hope that helps.