SINUSITIS
The sinuses are bubbles in the bones of our skull. They make our voices deeper. Mucus is also made inside of them, which drains into our nose. If the drainage pipe gets clogged up (often from a viral URI, or from allergies), the mucus pressure builds inside the sinus. That hurts. Stagnant fluid always gets infected, and the sinus is no exception. So they have a fever.
Most sinuses have drainage holes at the bottom of the bubble; however, the maxillary sinus is the exception. Its ostia is at the top, so it has to fight against gravity to feed mucus into the nose. It drains through the middle meatus (the superior meatus drains the sphenoid/ethmoid, the middle meatus drains the maxillary/frontal/ethmoid, and the inferior meatus drains the nasolacrimal duct). Interestingly, humans have evolved a relatively flat face that makes maxillary drainage difficult, hence our predisposition to sinusitis.
Sinusitis can be either viral or bacterial. You should suspect a bacterial cause if the infection (a) has lasted over 10 days, (b) has gross yellowish snot and (c) has a fever. The most common bugs are Strep pneumoniae (most common), H. influenzae and M. catarrhalis. After waiting through 10 days of symptoms, you should treat with Amoxicillin (for the first infection) or Amoxicillin / Clavulanate (if the Amoxicillin doesn’t work).
The sinuses are adjacent to the orbit and brain. Serious untreated infections can sneak into those places, causing orbital cellulitis, cavernous sinus syndrome or meningitis.