Have you tried calling, or going in directly to speak to them? A lot of the times it is easier for these places to reject you over email than it is actually speaking to you. Some hospitals have volunteer application forms, so check your local hospital's website for that, as the two hospitals in my town both had applications open.
A lot of people have volunteered at St John Ambulance in the past, which will depend on where you are though.
Could also try charity shops IF you can't find any healthcare related volunteering. Or volunteering in school, a lot of people I know volunteer to tutor younger years, anything like that.
Any sort of volunteering that can show you've learnt something, like a skill, will be helpful and is better than nothing, but I would recommend going and directly speaking to people in care homes & hospitals.