My daughter had severe allergic reactions to many things when younger (she's 16 now) & still has to be careful but once she began to ssort out what to keep clear of things gradually improved - other people need to see a skin &/or allergy specialist to get help - have you done this??
Have you experimented to find creams that help - both my son & daughter found that they reacted very badly to the usual creams etc that specialists give kids with eczema/psoriasis etc so everyone is different & you need sometimes to just figure it out by trial & error.
Those who laugh or tease though will do it more if they know they've gotten to you & less if they think you don't give a damn about thewm & their teasing/bullying. Good luck.