I have jaw muscle pain on the right side of my face and worsens when laying down. There is no pain when I'm standing?

Source of pain. Laying down will increase the blood pressure to your head which can increase pain stemming from your jaw bone. This is common with tooth abcesses. Also, head position can effect the sinuses. The muscle pain may come from pulling on the muscles differently, associated with side you lay on, or holding hand under your jaw, etc. Oral occlusal guard may help.
TGN. If you lay down you put pressure on that side of your face. It is quite possible you are compressing a nerve close to the surface. Another possibility is trigeminal neuralgia. Also known as tic delaroux. Get it checked out with your dentist or md. If it is the later...It could be very painful. Also...Just a note...Could be your sinuses misbehaving.