can a body rash be associated with a vanerial disease or can exema be communicalbe?

Son had a venereal disease, followed by a rash on arms back of hands front & back if torso & legs. Now his 4 yr old has it, it was diagnosed as exema but I don’t think it is… Therefore I am asking if there’s a home remedy that would clear it up or is there a possibility of it being something else?..

Concerned Grammy