I think you just have to manage your time , make a schedule of the things you're going to do . Like you can still study while watching your younger sister at home . Or at night you can help them sleep early by telling them bed time stories. If you do have other sibling you can ask for help too if you want tell them that you need to do important things im sure they will understand you . It maybe a challenging job for you but at the end of the day you will learn something from it .
You can lure your mind into really being productive. When I was studying, I used to have lots of extra curricular activities and I'd always jot things down. This should be done by this time and as much as possible, I try to stick with the sched. It will really help if you organize your to-do list.
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If your family is financially able, look for a nanny that will surely free-up some time that you can allocate to rest and study.