According to given data by you, the problem seems to be the symptoms of Trigeminal neuralgia
which is the disorder of Trigeminal nerve
that supplies majorly to eye, maxilla
and mandible but actually the pain of the Trigeminal Neuralgia would be more intense(burning, shooting, excruciating, shock
like pain) along with lacrimation of eye and may also limit the muscle movement.
For the sinus infection
there won't be much pain like prickly, burning, but you would have more headache and tenderness. Using medications like painkillers would decrease the pain for you but this would be temporary treatment and does not actually solve the problem. Please seek a Neuro-physician before the pain worsens.
All the Best and have a good Health.