I see your situation, thanks for explaining, What I would say is, could you not ask your older sibling to do their own research if you are so busy? It is very kind of you to research for them, but this information sounds much more relevant to them at this time, as it seems you are not even in Y11 yet, and it is important you do not over-burden yourself with responsibilities.
I also play an instrument quite seriously, and I also get involved in the music stuff at my school, as well as speaking in assemblies quite often, so I get your experience. What I would say is, you won't have to go to many open days and they only last an evening, so I think you will have time to attend them, don't worry about that (I attended 2 open days). Also, you should be proud of yourself that you're the main student in your year that does public speaking and performances - especially the public speaking will be very useful to you in your uni application for communication skills - so keep this up. But if it is affecting your academic performance, don't be afraid to explain this to your teachers as well, as your exams are the most important.