Ok, so your brother decided to use your email address, no doubt just to be difficult, but, that problem is easily solved by changing your password. I feel for you when you say your the only one who is there for your parents , I was the same as my sister didn’t want to know , but, while my sister has had to live with her conscious , my conscious is clear , and that means everything.
You sound a nice kind person , and very strong person also , which is good , so, just ignore your siblings , and do what you feel is the right thing to do , at least then at the end of the day you know that you did the right thing and your conscious will be clear . x