Killing potential yeast

I got a really nasty yeastie at the end of my period this month and I'm worried my cup may have some lingering yeast - I generally only boil it between cycles.

Will hydrogen peroxide kill yeast/is it safe to use on the cup? If so how much should I mix with water to soak it? Or can I just wipe it down? Would also be nice to remove the discolouring around the top of my cup while I'm at it.

Thanks for the help.