Poor Bowzer, it looks like he is having an allergic reaction. He should be see by a veterinarian so that they can administer allergy medications and control his symptoms. Other signs of allergy include a swollen face, vomiting, and lethargy in addition to the hives you are currently seeing.
More severe complications with allergies include difficulty breathing.
Please have Bowzer evaluated by a veterinarian as soon as possible so that he gets medications. Hope this helps and best of luck.