Whenever i move my eyes to the right, i have bad pressure behind my left eyeball in my head. what could this mean?

Inflammation: Pain or pressure on eye movement can indicate inflammation or infection within the orbit, inflammation of eye muscles or of the optic nerve, sometimes sinus inflammation, and other causes. These conditions require an eye examination to diagnose and treat, and sometimes imaging studies such as a CT scan. With significant discomfort, and especially double or blurred vision, get seen ASAP.