Bullet rating fluctuations I play on chess.com and I noticed that at some times I am getting beaten by 1700 pretty easily but other times I can beat 1900 with almost no effort. I broke my record and passed 2000 in bullet recently, now I am fighting with 2000 and 2100+ bullet players. Also, I nearly broke 1900 in blitz.Can I say my game has improved? I recently started to do tactics on chess.com, and it might have to do something with it. 

But the problem is when I play my brother OTB, I am slightly better, but he is 1300 blitz rated on chess.com. What is going on with my game?
Bullet is completely different from OTB game. In bullet what tells is your experience, your ability to spot hanging pieces and combinations very fast to make natural moves and not to blunder. Also time management and focus is very important. 

In an OTB game things like positional knowledge, and long term thinking are very important, and if it takes you a few minutes to notice, that the move you want to make hangs your queen, it's not a tragedy. Also you can get away with holes in your opening knowledge.

Another point: in bullet setting traps can earn you a lot of points, but in a long game traps are a lot of times counter productive.