If your work offers you EAP - you could call them - they have people that can talk with you on the phone (counselors) that can maybe at least calm your guilt/fears. Also many health insurances now offer telehealth where you could likely talk to a counselor immediately or close to it.
I am not saying you may need counseling yourself but they can talk with you and give you a venting ground and help you work through the feelings of guilt.
I've personally used it in that way without meaning to - when calling for some other advice - they actually helped calm me down when a family member was having some mental health issues.
Yeah unfortunately where your wife is an adult - it is up to her to allow you to have any information. I can only imagine how frustrating it must be for you - I wonder if you could try to reach out to the hospital again and ask to talk to her doctor - not about your wife but to provide some detail that maybe could be helpful for your wife? You could rely what happened and how sorry you are - and the doctor could decide if giving this information to your wife would help her.