Can I want be distant with my parents/family?
I hope everything is alright. What do you mean when you see "be distant"?
I want to always be busy so I can stay away from them
Its fine to want to be busy so you can achieve your goals and aspirations, however being busy just to ignore your family is the wrong reason. If you are upset with your family your best bet is to just tell them so you are not weighing down your mental.
Alright, see you.
Trust me when I say this. It's best to have your family around because they are the ones that will have your back if anything were to happen to you. Don't give up on your family for some personal reasons or if you think they are annoying, because there are a lot of people in the world that don't even have a family.