A 40-year-old female patient presents with fever, generalized joint pain, and purpuric rash for 1 year. She has a 2-year history of recurrent bronchial asthma and allergic rhinitis. CBC shows: WBC 10.1×10⁹/L (neutrophils 68%, eosinophils 16%), elevated immunoglobulin E (IgE), and p-ANCA positivity. The most likely diagnosis is: