I am glad you are reading into such detail, it has made me revise anatomy, thanks to you! So if you don't have trigeminal neuralgia and just TMJ symptoms, do not worry about the report. A vein of the venous sinuses could very well pass near the nerve (its a rather extensive network of veins). Also, the pressure of blood flowing through veins isn't all that high as the artery, so it wouldn't damage your trigeminal nerve.
Next Steps
So, next steps - depends on your symptoms, for TMJ pain, some analgesics will work. For Hemifacial spasm, we have medicines, and later, botox if medications don't work.