In this context, "I'm gonna throw my shit around!" means to throw one's strength or power around right before they're about to do something badass.
"I'M GONNA THROW MY SHIT AROUND!!!"
"I'm gonna throw my shit around" in this context means to throw one's weight or power around, it is typically said right before doing some kind of impressive move or big attack.
"hold on lemme charge up an attack... I'M GONNA THROW MY SHIT AROUND!!"