Methotrexate, Erlotinib, and Celecoxib for the Treatment of Recurrent/Metastatic Head and Neck Cancer in a Rural Midwest United States Population

Inclusion Criteria: * Age ≥ 18 years * Histologically confirmed diagnosis of relapsed/metastatic head and neck cancer, including oral cavity, oropharynx \[human papillomavirus (HPV) positive and negative), hypopharynx, and larynx cancer * Measurable or non-measurable disease is allowed * Measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) criteria * Non-measurable disease * NOTE: Other nonmeasurable lesions include clinically evident lesions not well visualized on imaging \[e.g., oral cavity mass readily seen on physical exam but obscured on computed tomography (CT)\], dermal metastases, and bone metastases * Prior treatment: * One of the following must be true: * Received standard 1st-line immunotherapy or chemo-immunotherapy OR * Unable to receive or refuse 1st-line therapy * Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0, 1 or 2 * Hemoglobin ≥ 9.0 g/dL (obtained 15 days prior to registration) * Absolute neutrophil count (ANC) ≥ 1500/mm\^3 (obtained 15 days prior to registration) * Platelet count ≥ 100,000/mm\^3 (obtained 15 days prior to registration) * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (obtained 15 days prior to registration) * Alanine aminotransferase (ALT) and aspartate transaminase (AST) ≤ 3 x ULN (≤ 5 x ULN for patients with liver involvement) (obtained 15 days prior to registration) * Prothrombin time (PT)/international normalized ratio (INR)/activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN OR if patient is receiving anticoagulant therapy and INR or aPTT is within target range of therapy (obtained 15 days prior to registration) * Calculated creatinine clearance ≥ 45 ml/min per Chronic-Kidney Disease-Epidemiology (CKD-EPI) Creatinine Equation (obtained 15 days prior to registration) * Estimated creatinine clearance (Clcr) by the CKD-EPI Creatinine Equation (per National Kidney Foundation) (obtained 15 days prior to registration) * Negative pregnancy test done ≤ 8 days prior to registration, for persons of childbearing potential only * Provide written informed consent * Ability to complete questionnaire(s) by themselves or with assistance * Ability to swallow pills * Willing and able to adhere with the protocol schedule for the duration of the study including undergoing treatment, attending scheduled visits, and examinations Exclusion Criteria: * Any of the following because this study involves an investigational agent, the genotoxic, mutagenic, and teratogenic effects of which on the developing fetus and newborn are unknown * Pregnant persons * Nursing persons * Persons of childbearing potential and persons able to father a child who are unwilling to employ adequate contraception * Uncontrolled intercurrent illness including, but not limited to: * Myocardial infarction ≤ 6 months prior to registration * New York Heart Association (NYHA) class III or IV heart failure * Corrected QT interval (QTc) prolongation more than 440 ms in males and 460 ms in females * Uncontrolled dysrhythmias or poorly controlled angina * History of serious ventricular arrhythmia \[ventricular tachycardia (VT) or ventricular flutter (VF)\] and/or factors that predispose to arrhythmia (e.g., heart failure, hypokalemia, family history of long QT syndrome) * Ongoing or active infection requiring systemic treatment * Active gastrointestinal bleeding * Psychiatric illness/social situations that would limit compliance with study requirements * Immunocompromised patients and patients known to be HIV positive and currently receiving antiretroviral therapy * NOTE: Patients known to be HIV positive, but without clinical evidence of an immunocompromised state, are eligible for this trial * Known hepatitis * Exception: For patients with evidence of chronic hepatitis B virus infection the hepatitis B (HepB) viral load must be undetectable on suppressive therapy, if indicated, to be eligible * Exception: Patients with a history of hepatitis C virus infection must have been treated and cured. Patients with hepatitis C virus (HCV) infection who are currently on treatment are eligible if they have an undetectable HCV viral load * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Other active malignancy requiring therapy such as radiation, chemotherapy, or immunotherapy. Patients on hormonal therapy for treated breast or prostate cancer are permitted if they meet other eligibility criteria * NOTE: Patients with secondary malignancy with life expectancy ≥ 2 years are eligible * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens