Thanks for writing.
After reading your symptoms, I feel that you may be having an attack of trigemminal neuralgia
The features in trigemminal neuralgia are similar to what you say, pain on one side of the face, may involve eye and jaw also.
The reason the pain is more while sitting or lying down is because there may be a blood vessel close to the course of the trigemminal nerve
and touching it when you sit or lie down. This results in pain and when you are standing, the nerve is free.
Please consult a neurologist
and he will examine you and give you medication.
Hope this helps.