He may be hemophiliac? Or the random bruising is also a symptom of some cancers...not trying to scare you. Biting him into a derm and maybe they can figure out what is going on. Best of luck to you both!
Unexplained bruising of the arms can be caused by medication, liver disease, bone marrow cancer, and hemophilia. It also common with illness that affects platelets, like thrombocytopenia.
The right move is to take your boy to the doctor -- an pediatrician or internist , who will need to make blood tests to diagnose the problem.
Best wishes for your boy.