Why is my Diadora Traccia's rear tire rub against the frame
There's no such thing as a "left axle" and "right axle": your axle has snapped in two. Replacing it yourself will require specialized tools for the bearings and to remove and replace the rear sprockets: unless you think you'll use those tools again in the future, it's most likely cheaper to get a bike shop to do the repair for you. Or look to see if there's a bike co-op in your area.