I'd like to 👍 what some other people have been saying: you don't HAVE to volunteer in a hospital. Volunteer at a place you would be more useful
I volunteer at a hospice residence, which is basically a big house with a nurse 24/7 where people come to die peacefully if they can't stay at home and don't want to be in a hospital. I agree with other people that people in duress often like to be sat with. One lady at the home (who's actually been there a while) just doesn't like to be alone. She loves for me to come sit with her, even as she falls asleep. I feel useful because I'm helping someone die they way they want, I'm helping bring them comfort/peace, I'm there to talk about whatever they like and won't judge, etc. I feel like I'm actually HELPING people - even if it's just a little bit, when you're dying/very ill, every little bit counts, in my opinion. Today was a quiet day when no one really needed me at all, so I baked a chocolate cake and frosted it. I know the residents will get to eat it, as will the staff, other volunteers, and visitors. Yayyy bringing smiles to people!
If you reeeaaaallly have no other options...I emphasize that there is a floor on every hospital with people who are under great duress and could use company - the ones who keep asking for nurses, the ones who have no idea what is going on, the ones who just want to be heard (but I don't expect nurses to hear them all day long). Your presence would be useful to these people, and it could be a nice exercise in stretching your empathy reserves and not becoming frustrated.
Nursing homes are also places that will have patients/residents who could just use some basic help (like with eating) and company. Eh, I suppose I don't remember seeing volunteers at my grandparents' nursing home, but I'd hope that would be because it's a seriously unpopular place to volunteer and they live in an area with low population density rather than because of liability fears.
But what I most want to say is: If you don't feel useful, find somewhere you do! Volunteering can be such a joy.