Sounds like you can sense there's something going on with your sister, perhaps based on more than just the cuts on her ankle. Your sister's so fortunate to have someone so sensitive in her life.
Having lived with depression for a number of years earlier in my life, I can relate to that feeling 'It's all my fault'. It wasn't until much later in life that I realised being sensitive is not my fault, it's actually my ability that allows me to get a sense of what or who's bringing me down or what's stressful. Our sensitivity allows us to also feel when we're in a significant challenge that we may need help with. It can take a long time to come to exercise our sensitivity in positive ways. Btw, when people say 'Toughen up', what they're really saying at times is 'Stop accessing your ability to feel'. I imagine you're pretty sensitive/intuitive, which may help explain why you can sense there's something off regarding your sister. Addressing whether the scars are related to past issues resolved or they're linked to ongoing issues is the question.
Is your sister as sensitive as you? Do you think she can feel what's depressing or she can feel what's challenging but she can't necessarily identify the factors involved, those which lead her to feel so intensely? With sensitive people typically being 'feelers', using the language of feeling can help make some difference. Eg: Instead of 'I think I need to ask you if you're okay. I think there's something upsetting you. I think we need help with this', how would it sound if you were to say 'I feel the need to ask you if you're okay. I feel there's something upsetting you. I feel we need help with this'? This is one way to lead a person to understand you truly do feel for them.
While your experiences with depression are not your fault, it's also important to remember how hard you've worked to get through what's not your fault. I know you've worked hard because I can relate to how incredibly demanding and exhausting the battle can be, especially the very depths of depression. You should feel proud of yourself.
If you imagine you can't approach your sister at all without feeling significantly triggered, is your mum an easy person to bring this concern up with? If you're mum's sensitive also, she may be triggered by this. I'm a mum, we're easily triggered :) It still remains our job to be guides for our kids, especially through the toughest of times. Your mum may need to employ someone to help her if need be.