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Hello. Thanks for the question.
The panting may be a vaccine reaction or a reaction to one of the meds. Of the meds, Simplicef would be more likely to cause a reaction. If you want to try to give something to blunt that response, you can use Benadryl at home. The dose of Benadryl in dogs is 1-2 mg per lb body weight. It can be given every 6-8 hours, as needed.
I would hold off on giving the meds tomorrow, and talk with your vet to see if s/he would like to change either one or hold off on either one. If the Simplicef is not absolutely needed, then I'd probably stop that one. Apoquel is more of a chronic med, and I would give that another chance as it can be great for allergies in dogs.
I hope this helps, let me know if you have any other questions.