Can a sinus infection or an ear infection cause neck pain, more specifically, the lymph nodes? is this a normal occurrence?

Yes: Infections in the head, including ear infections, sinus infections, and tooth infections, can lead to swelling of the lymph nodes and pain from the inflammation. They usually take a few days to a few weeks to fully resolve. Please see your doctor if they are especially large and painful - or if your neck hurts when you bend it toward your chest.

Unusual: Otitis media (ear infection) or rhino-sinusitis rarely cause neck pain or cervical lymphadenopathy. Certainly this is possible and only means that the lymph nodes are a protective mechanism to prevent further spread of this viral/bacterial infection.