First things first, the pain in your shaft when you are urinating. That can be a sign of a lower tact urinary tract infection. https://www.healthline.com/health/pain-in-middle-of-shaft. You're gonna need to pee in a cup so they can check for bacteria in the urine. But then you have this vein also. We can get a little clot in the vein there and that also can cause some pain in the shaft. Penile clots also cause both pain in the shaft and a bulging vein. This sound about like what is going on? Clots in the penis usually happen in the dorsal vein which is on top? this where it's at? Thing is, you'd probably have pain when you get an erection too. Either way, I do think you need to see your doctor since you have not just a vein but pain. Docs are doing work over the phone and virtually a lot lately so give yours a call. If you don't have a regular doc, then urgent care. That sound like a plan?