The decision on what anti-inflammatory medication to take for swelling and pain in the upper jaw to get better quickly depends on the specific cause that triggered the symptom.
If the symptom is caused by a bacterial infection, an aggressive application of antibiotics will give a better outcome.
If the symptom is caused by a viral infection, antiviral medication is usually indicated.
If the symptom is not caused by an infectious disease, a specialist visit to determine the cause will determine the treatment plan.