I would hold off on medication until you've tried the new food for at least two months to see if the itching and hives go away.
Like most hounds, Beagles were bred to hunt and work independantly and make their own decisions. They are not stupid, they are just so intent on following scent that it's difficult to get them to focus on anything else.
Even the most well trained Beagle is likely to bolt when off leash, so don't be lulled into a false sense of security and let her run loose.
