Hello Thank You for contacting HCM. Talking about your first question, side effects(most common) of celebrex includes: headache, hypertension, fever, dyspepsia, cough, vomiting, diarrhea Both drugs you mentioned in description are used to relieve pain. Talking about hives, yes they can cause allergy. Back pain has normally no connection with allergic response. Hope this answers your question. If you have additional questions or follow up questions then please do not hesitate in writing to us. Wishing you good health.