Seems like one of two things are happening. While broadcasting its eating up a lot of CPU or memory and the game's just compensating. The only way around that is a more powerful computer.

OR the other programs you're using have a throttling mechanism setting your MAXFPS to 30. Just in todays patch notes-

Technical
  • Frame Rate: A maximum capacity of 200 frames per second has been added. To disable the frame rate limit, the following line should be added to the Config.wtf file: SET maxFPS "0".
Just a side note you can set it to any number you like- 0 is just means unlimited. So if you want 60 set it to 60.