Welcome to the STD forum. The bottom line is that no STD is likely to be the cause for such a symptom.
You don't say anything about your sexual activities or other risks for STD. And apparently you have no other STD symptoms, like genital ulcers, penile discharge, etc. But even if you are at high risk, I doubt this symptom is due to any STD. There is a ligament that runs from the pubic bone to the hip, so maybe that's just a little more prominent. Anything serious, like inflamed lymph nodes, would not be so symmetrical, with nearly identical appearance on both sides of the body. I also doubt this has anything to do with your hernia. And apparently there is no pain or tenderness, which also suggests this is nothing abnormal.
However, it is impossible to tell what you have with certainty, without direct professional assessment. Without direct examination, you will never get a definitive answer, so see a health care provider.
Regards-- HHH, MD
Do lymph nodes move or expand when you cough? As for the vein-like ligament, i think what you are referring to is the inguinal ligament, but my understanding is that this band is deep inside the body. So is it normal for this to be visible?
Furthermore, don't the superficial inguinal lymph nodes appear as a chain that might resemble this cord? I'm worried it might just be that.
Thanks again.
Please re-read my reply above, which is intended to be reassuring. My guess is that this is nothing serious and perhaps nothing abnormal at all. I will be happy to comment again after you report the result of a professional examination -- but until then will have no more to say.