Okay so, I recently stopped using my brother's account and got my own. When I logged in, I went to single player to make my world, I saw all the worlds from my bro's account. How is this possible? The two accounts have NONE of the same info! Then I go to multiplayer and try to join sabotage, and it said, "Failed to Login: Bad login". I login on my bro's account, try to join sab, and same thing! Same with all other servers..... Can someone... ANYONE PLEASE tell me why this is happening? And how do I fix it? I'll give you diamonds!!!!
You are both using your accounts from the same computer so you are sharing the files in the .minecraft folder, the saves (worlds) are for both of you, the minecraft.jar file is for both of you (so if one adds a mod the other is stuck with it too). You just have a separate login, username and skin for playing multi-player online, but your sharing the one single game install. The only way I know of to change that is to make your own copy of the .jar file and saves folder and make one for him and swap them out before one of you plays.
I know that sounds like a pain but the game just is not really designed to be shared on a single computer.
As to why your login is failing I haven't got a clue, either of your logins should still work and you trying to login via your new account password should not have changed anything. Sounds as though maybe you need to delete the bin folder and lastlogin file from inside the .minecraft folder and then start the game again so that it downloads clean copies. It can't hurt anything to try it...