What does "我牛起来" mean?
“我牛起来” means “I’m gonna be better/successful/cool”
In this sentence, “牛” is short  for “牛逼” which is meaning of  “super cool”.
Why does “牛逼” mean “super cool”? You could find the answer in this video
https://youtu.be/teQPusK7YFU