It would be unusual to be allergic to only one specific dog! Typically a person would be allergic to an entire species. Does this puppy get treated with a specific spray or skin treatment that the other dogs do not get? At any rate you should check with a human dermatologist for this problem.
Training a puppy to be less destructive is a real battle. First, always have dog toy alternatives to offer your puppy when stopping destructive behavior. Also, never offer “old shoes” as a replacement for “new shoes”; your puppy cannot tell the difference. Consistent scolding and a firm “No” coupled with offering a dog toy will show results. Time is on your side, the puppy will outgrow this destructive behavior.