Answer: A sinus infection can cause neck pain.
More Info: The symptoms of a sinus infection depend upon which of the sinuses are infected. Neck pain is associated with an infection of the sphenoid sinuses. 
What Are Sinuses?
The human skull contains four hollow interconnected cavities called sinuses. The maxillary sinuses are in the cheekbones, the ethmoid sinuses are located at the bridge of the nose between the eyes, the frontal sinuses are located in the forehead, and the sphenoid sinuses are located in the bones behind the nasal cavity.  Sinusitis occurs when the mucous membranes lining the sinuses become inflamed a block the drainage of mucous. An infection in any one of the sets of sinuses will carry with it distinct symptoms based on its location. Neck pain is associated with a sphenoid sinus infection.
What Is Sphenoid Sinusitis?
Sphenoid sinusitis is an infection of the sphenoid sinus, a deeper sinus located behind the nasal cavity. This rare, acute sinus infection is accompanied by severe headaches — its primary symptom. The headaches tend to worsen with changes from an upright position, such as, leaning forward, stooping or reclining. Due to the close proximity of the sphenoid sinus to the optic nerve, visual complications typically occur in the form of blurred or double vision. Sphenoid sinusitis is extremely painful and difficult to treat. A long-term antibiotic treatment or ear, nose, and throat (ENT) specialist may be required to cure the condition. 
Can a Sinus Infection Kill You?
Though not common, a sinus infection that is located in the ethmoid or sphenoid sinuses can spread to the brain. The symptoms of this sinus infection complication are altered consciousness, mild personality changes, vision problems, and can even lead to seizures, coma, and death. 
How to Prevent a Sinus Infection
If you want to follow basic rules that teach how to prevent a sinus infection, you should know that the most basic rule is to wash your hands often. Avoid cigarette, cigar, and pipe smoke since smoke causes and irritates inflamed membranes in your sinuses and nose. Avoid breathing dry air and consider using a humidifier to increase moisture in the air. If you have stuffiness caused by a cold or allergies, treat it promptly to prevent a bacterial infection from developing in your sinuses. If you have allergies, avoid things that trigger them. You may want to consider taking allergy shots. 
 Asthma and Allergy Foundation of America.
Human Anatomy: Sinuses
 Cleveland Clinic-Center for Continuing Education
 University of Maryland Medical Center
 National Library of Medicine
“Although the sphenoid sinuses are less frequently affected, infection in this area can cause earache, neck pain, or an ache behind the eyes, at the top of the head, or in the temples. In addition, drainage of mucus from the sphenoid down the back of the throat (postnasal drip) can cause a sore throat and can irritate the membranes lining the larynx.”
An unusual presentation of sphenoid sinusitis with septicaemia in a healthy young adult Emergency Medicine Journal
“Sphenoid sinus opacity is mostly inflammatory in origin. Despite the benign nature of the disease, there is a risk of complications with high morbidity and mortality. Early and, if necessary, aggressive therapy to guarantee drainage of the sinus is recommended.”
Isolated Sphenoid Sinus Diseases JAMA Otolaryngology-Head & Neck Surgery