I don't get neck pain as you describe when I get my own sinus infections, which for me, seem to be seasonal.
Many people and doctors, get this confused with a common cold or allergies. If you know for sure you are experiencing a sinus infection, then the usual treatment should apply, which is antibiotics for bacterial sinus. While the common cold is a viral infection and allergies are a reaction to a histamine release, which require anti-histamines.
Many times, your symptoms can start out with a sore throat, a cold or an allergy to like pet dander, then turn into an infection when things get clogged up by mucus, usually mucus gets trapped in the passages and bacteria builds up behind the block because of poor drainage.
I believe the soreness in or around your neck you are feeling just prior to sinus, is the lymph nodes swelling, these nodes, located throughout our bodies, are the indicators some infection has invaded a certain part of the body that particular nodes it controls. They are like a "catch basin" when a major infection gets into the blood stream, I suppose the reason for the usual swelling.
When you see your doctor and you tell them you are experiencing neck pain, first thing they always check for is swollen lymph nodes by feel, massaging the neck areas. The doctor should also look directly into your nose with a light scope, they either see the blockage or the discoloration of the mucus or both.
I would def see your doctor if you cant get the clog cleared yourself, the bacterial infection will just get worse
I had one case of bacterial sinus infection I was able to dislodge my self, it was gross. After you get the stuck mucus out of your sinus, you usually end up swallowing it where it eventually will come out when you hock it out, im my case, the blockage was a quarter size bloody mucus blob that came out when I spit, gross! But it saved me a trip to the doctor for antibiotics, which will do the same thing but just faster. Invest in a neti pot as well