Do what makes you happy, not based on what other people think. If people think you are strange then they're probably not worth knowing anyway. But if I had to answer I would say no, it's not too strange. I think it's cool that you've got a variety in your lifestyle and personality.
I don't think you'd be allowed to wear them while you cheer, so you'd have to stop doing cheerleading for a few weeks-months while they heal. also, they might affect your flute playing. Overall I'd say don't do it (for the above reasons) and also because I'm just biased and don't like snakebite piercings. It would probably be a strange combination for you.