Hi Christie0909,
Welcome to the forums! I’m sorry to hear your credit was ruined because of medical reasons. That’s not fair. I think health care in this country needs a drastic change, but that’s a topic in itself. Hopefully everything went well with your surgery and your now healthy which is the most important thing.
About the secured card. I got the Capital One card with a lower credit score than yours, plus I have bad credit history so I think you should be able to get it as well. I don’t think living with your parents will be an issue when applying for this card. I remember somebody commenting on the blog was in the same situation and was approved (if I remember well this person reported paying a little bit of rent, you may want to check the blog comments for this info).
Luckily you are still young so you have time to rebuild. Trying to do something about it and informing yourself about how credit works is the first step so you are moving in the right direction 
You mention that there are two reasons that you are still hesitant. I would happy to try to answer any doubts you may have. And thanks for sharing your story!