Technically it is not your job to find coverage. If you need to call off, you can help. But it is literally within policy that the shifts/SM are the ones responsible for finding coverage for you. You may get crap for it, but in the end it really isn't your responsibility.

Jeez that’s tough. I’m also trying to get a shift covered! Honestly it depends on the manager. I had a tough time a while back when I first started working at my second store where I forgot to come in when I said I could cover a shift, and then someone didn’t come in when they said they could cover for me. My manager had a talk with me after my next shift. I thought she was SO MAD based on the text she sent me but she was really sweet and told me it would take a while for the rest of the partners to regain trust in me although everyone loved working with me.
Well anyways she was fired last week so who knows now but my advice is be apologetic, have a plan to talk about how to avoid this in the future, and don’t feel too bad - you did everything you could and you’re a student first!