Having worked for a vet dermatologist for years I can tell you that first off dogs cannot get poison ivy they are not affected by the oils but can transmit them to humans. Whenever I hear someone say hives or rash in a dog I chuckle because dogs don't get that either what you ARE seeing is bacterial infection of the skin which means you pup needs to see a vet asap and get some antibiotics to systemically clear things up. Finding the underlying cause is another issue to discuss. Allergies can be the number one cause but you also need to rule out other possible issues. Find a good vet to discuss this with because spinning you wheels with an inexperienced one will only empty you wallet on unnecessary things. If you can't afford a vet dermatologist have your vet call and consult with one so they can steer your vet in the right direction. Pugs and beagle I can tell you we see alot of due to allergy infections so it's no wonder a puggle is having issues. Here are some tips for allergies: shampoo frequently, wipe down with baby wipes when he comes in from outside or even have him wear a tee outside. If it's environmental then allergy shots work great but try controlling with baths, wipes, antihistamines 1st. Sometimes 1 antihistamine will work great for awhile and like people you then may need to switch to another. Atopica is a drug that can be costly but very effective. If it works then usually a dog can go to the generic cyclosporine which is a human drug and you can shop around online for it. Also they cna be weaned to a smaller dose over time which is much more affordable. Food allergies are also something to think about and for that I'll defer to some earlier posts I have made to people about elimination food trials. The main thing about allergies is find the route of the problem otherwise you'll spend many years and money on clearing up skin infections with antibiotics and vet bills. Good luck! Any other ?'s please post me a note to my profile :)
I forgot to mention my dog is a Puggle. Pug/Beagle