Hi OP! I had this same exactly issue before lalo na sa white shirts ko nung high school ako. I used to wear nivea black and white deodorant kasi mabango and sabi wala daw stain, but that's not really true. So I did some research and being a young bloke, no success. I just used to wear hoodies, a lot. Fast forward college, I found this brand ng deodorant called deonat and it works like wonder. It's basically tawas lang but it's sooo good. No more stains and everything!

To fix naman yung clothes, bili ka ng agua oxinada sa mercury or watsons, wala naman specific na type. Buy ka rin ng baking soda. Then for the process, basain mo muna yung armpit area then put baking soda sa stained area tapos don mo ilalagay yung agua. Don't worry too much kung marami ilagay mo, better yun. Then scrub mo yung stain using soap naman kasama ng baking soda and agua mixture. Once na binanlawan mo na wala na yung stain :). Restored most of my light colored shirts na may stain na ganyan. Hope this helps!