Here's my follow-up after my visit to the GP. He told me to get X-rays done of my head and neck to check for sinus and spondylosis. I got them done and it seems that there's no problem with my sinus. But it turns out that I am showing signs of Early Cervical Spondylosis.
The doctor showed me a simple neck exercise to do. But I don't think that's enough. Because the pain and discomfort keeps returning intermittently.
I am going to consult a specialist doctor in this field i.e. an orthopaedic surgeon. I will let you guys know what happens.