Trigeminal neuralgia is a chronic pain condition that affects the trigeminal nerve. The trigeminal nerve carries sensation from your face to your brain.
Im not surprised that the pain brings about tears because the pain is often described as excruciating.
I'm wondering if the condition is more prevalent on that side for a reason associated to your specific diagnosis or the location of where your nerves are.
Have you asked your doctor about it? Has it always been this way it is this a new development?