Hmm, hydrogen peroxide is a weak acid and an oxidizing agent. By weak acid, I think it means it has a positive charge and lets say the worms or any fungi or bacteria on your skin have a cell membrane with a negative charge, since opposites attract, it will tear their cell membranes apart and they will die. Now, if their eggs or spores are of the capsule sort, these are generally very tough and I don't know if the peroxide would penetrate them or not but it would most def. affect the adults.
It's also extremely reactive so the most important advise that I can offer you is that you should use it alone since you don't want an acid base reaction having on your face or inside your pores! Also, could the hydrogen peroxide be reacting with some leftover material from the masks which you are doing? Remember, hydrogen peroxide is a bleaching agent, so just like it bleaches the skin and hair, it'll most likely bleach clay or earth or anything white and then by reacting with it, cause it to shoot out of your pores.