Hardened vein from bottom to top (full length) of penile shaft during erection. discomfort during sexual intercourse. it's a smaller vein beside the main big vein?

If both go away or become much smaller when not erect the veins are distended because the muscles in you veins contract so blood cannot get out of penis and that causes the erection. After orgasm or fatigue the muscles relax and blood flows out of penis. and veins are smaller because they are not damned up. Never heard of a vein inside of a vein. A picture would be good to share with us/your Dr.

Occasionally the vein gets thrombosed. But that resolves in 4-6 weeks. Wait for a week or two before trying sex then you wont have pain. If it does not resolve see a Urologist.