University application and shitty school

I need to find a university , I will go to uni from next year. But I will have to prepare applications earlier than this and submit it because those are the deadlines. I have hardly 2 months.
My summer vacations are going on and I will start school from July 1st
I planned to do all this during this time. It's not happening though , we are somewhere else , away from home , we are going out almost daily and my mom doesn't let me stay alone. So I have to be with them all the time. I try what I can but I don't see clear progress.
We reach back at our stay place by evening and then I just crash out because of the tiredness emotionally , mentally and physically.
I am also not planning to do my holiday homework because it doesn't get religiously checked and last year I felt I was the only one who did the work properly and yet it didn't got checked. Our principal is different this time and he's an asshole .
Some shit happened and I along with someone else protested against them ( the principal was part of our opposition ) so the thing is , I am probably in his bad eyes and if I won't do it , he may force me to do it.
But then I should do it ? But I think it's a waste of time . I am thinking of going to school , see how it goes , if I get a scolding or something we will see.
But it's a lot of holiday homework and if I would have to do it then it will be a lot.
Along with it , my studies are not going great.
I know this may sound like I am making excuse but I feel I could have done a lot by staying at home . Or by getting proper space and time.
I don't know how to manage it. I feel everything is crashing down.
I feel anxious but I know it's valid. June is almost gone..
When school will start again , I will struggle a lot with the schedule. I work slow , I have started two side things which are really important for me and I don't plan to give them up at all. I don't know how the fucking fuck will I make the whole application thing then. I also can't give up on my 8 hours sleep which is often romanticised because if I will , I will wake up like a dead person who is just breathing and somehow going through the day.
My deadline was June , the one I set for myself.
I don't think I can get any help , because a lot of context is needed I guess , regarding the timetable and stuff
But if you still have some advice I can truly use , please give me , I would appreciate it.
It sucks to be so anxious all the time. I feel I am wasting my life.

Ps. I am having some feelings with this website. If you ever disliked me just don't reply to this , I don't want judgements , plain replies for the sake of it , just don't.
Reply only if you truly want to , if you felt empathy , if you have any advice or something , not because you have to . Please.

Congratsbaby, you certainly have a lot on your plate, and it sounds like you're not getting much understanding or support. Your mother seems to have other priorities and your principal lacks understanding or sympathy. Why won't your mother let you stay alone? Are you able to talk to her about how vital this time is for your applications?

These side things sound important. Are they something you might be able to build a future life on?

I guess my last question is about this holiday homework you've been assigned. Is it mere busywork, or is it work that will give you an advantage in your courses next term?

Thanks , my mother won't let me stay alone because I think she has anxiety and is not secure to know that I will be fine alone and even though we are at our uncle's house and we have explored the local places here , they still go everytime we come here and for her this is vacation and so is for others so they all are like " you are to travel blah blah "
I didn't tried to tell her because I plan to tell my family members only when it's really necessary.
Yes , I do consider both of them to be foundations of something I really want to do in future. The benefits might come probably later on but I don't want to start something thinking about money only , like I am not that person. I get zero motivation when I think about money.
My Holiday home work is busy work only.
I might get a few advantage by completing my p.e work but I would still have to understand and learn so it would be just me copying shit so yes busy work for now indeed.