I am not a member of the union, so please excuse me if my response is off-base. But, don't unions have representatives and/or delegates available to members who need them? It sounds very much like you need representation. Normally I would suggest you obtain a labor lawyer, but as a union member try to get someone assigned to your case by the union.
Once you have representation, tell your entire story to them. Have them approach your employer and request complete documentation on your alleged offense.
It is likely that once they see the evidence, they will be able to poke holes in the story. If they succeed in completely disassembling the allegations as false, they can then officially request a retraction be placed in your HR file.