Left handed - Right handed drumming?

Hi! Im naturally a left handed person but I was in my school marching band I was taught to play right handed. When playing drums, I enjoy playing right handed, but when it comes to playing songs like Everlong by Foo Fighters (16th notes to snare) I mess up all the time. I am used to doing my fills by crossing my hands. But sometimes when I do, I miss the drum (too far away?). Is there a name for this kind of drumming? What do you recommend for me to switch to left hand drumming and start from scratch? Thanks!