@FireBoner could definitely be the case! The anatomy of veins is different from person to person. There are also some people in the adult entertainment-industry with such big dorsal veins as you stated, some even bigger. So it's normal

And if they are on the side and you put a very tight and big
cockring on, it could cause this problem. I'd use less tight ones or some which aren't that big and more thin. There's a reason why cockings also have sizes LOL hope that helps a little bit bro!