You're speaking to Dr. Michael Salkin. Welcome to JustAnswer. I'm currently typing up my reply.
I understand your concerns. As with any drug, the benefit to risk ratio needs to be assessed before it's prescribed. According to Plumb's veterinary Drug Handbook, 8th Ed., Plumb, 2015, "Due to its recent approval and limited clinical use, the adverse effect profile for oclacitinib (Apoquel) isn't fully known. Most commonly gastrointestinal effects (vomiting, diarrhea, anorexia), increased thirst or lethargy have been noted but other potentially serious adverse effects including susceptibility to infections (e.g., pneumonia, demodicosis/mange, neoplasia/cancer, and skin disorders are possible."
Your vet prescribed an immunosuppressant drug in an attempt to quiet down your dog's immune system related to its skin. Alternative immunosuppressants include the glucocorticosteroids such as prednisone, and chemotherapeutic drugs such as cyclosporin. Each has its own adverse effect profile. Which type of allergy is present, please? Perhaps I can recommend alternative therapies for it.