What could possibly be wrong if I've had a sinus headache for more than 4 days?

Congestion/ infectio. Sinus headaches often result from congestion that fills the sinuses. On occasion these too can become infected. You may notice tenderness when you press on your sinuses which may indicate an infection. Usually this is viral but your doctor may opt to prescribe you antibiotics. You may also try a decongestant like sudafed (pseudoephedrine) if able to alleviate your symptoms if it is congestion.
Sinus Headache. A sinus headache is common for more than four days. Most head colds last 5 to 7 days. Many allergy flareups last longer than four days. If the pain / pressure lasts longer than 7 days, go see your primary healthcare provider. I always recommend a short trial of topic nasal decongestants, but caution is needed, as tolerance is common, if use is prolonged more than five days.