This phase II trial studies how well celecoxib works through surgery and radiation therapy in treating patients with head and neck cancer that has spread to other places in the body (advanced). Celecoxib is Food and Drug Administration approved to treat arthritis, acute pain, and painful menstrual periods. Adding celecoxib to standard of care treatment may help to decrease the amount of time between surgery and radiation therapy.

PRIMARY OBJECTIVE: I. To assess the number of days from surgery to initiation of radiation with the addition of celecoxib compared to placebo. SECONDARY OBJECTIVES: I. To assess overall pain control and management for patients on celecoxib compared to placebo. * Subjective pain scores on the visual analog scale of pain intensity averaged over a week at rest, with a swallow, and with a cough. * Patient satisfaction with pain control questionnaire. * Narcotic consumption in daily total morphine equivalents averaged over a week. II. To assess functional outcomes for patients on celecoxib compared to placebo. III. To assess the effect of celecoxib therapy on Quality of Life (QoL) compared to placebo. IV. To assess the average number of treatment days missed during adjuvant radiation for patients on celecoxib compared to placebo. OUTLINE: Patients are randomized to 1 of 2 arms. ARM I: Patients receive celecoxib orally (PO) or via feeding tube twice daily (BID) starting 5 days prior to surgery and continues until the completion of radiation therapy (up to 6 months in total) in the absence of disease progression or unacceptable toxicity. ARM II: Patients receive placebo PO or via feeding tube BID starting 5 days prior to surgery and continues until the completion of radiation therapy (up to 6 months in total) in the absence of disease progression or unacceptable toxicity.