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Hello, this is Dr. Jess. I am so sorry to hear about your pup! If you feel like he is having difficulty breathing and unable to relax, then that may be a sign that a visit to an emergency vet is needed. Oftentimes in these cases, a steroid is required in addition to benadryl to get things under control. If he has large bumps those are likely hives, and a swollen paw as well, I think this in combination with his panting and excitement are worrisome. The other thing that makes me feel it is better to be safe than sorry is the fact that he is a bulldog, so he is a brachycephalic dog (smooshed face) which makes breathing already an issue for him, and if his airway becomes compromised, it is much more dangerous fast for him than a dog without this conformation.
So a trip to the emergency vet is definitely the safest choice for your guy.
Here is an article with more information for you: http://www.petplace.com/article/dogs/diseases-conditions-of-dogs/emergency-trauma-urgent-care/allergic-reaction-from-an-unknown-cause-in-dogs
Please let me know if you have any other questions. If you do not, please take a moment to CLICK AND RATE our conversation so we can know if you were satisfied with your service and I can get credit for helping to answer your question. Thank you and best of luck!!!