Last weekend I had sex with my girlfriend that lasted for several hours. I have placed a robber-ring at the base of my penis.

My partner has used oral and (somewhat rough) hand stroke on my penis at the end of our sexual act.

Few hours later I noticed some swelling of the lateral veins, the veins became thicker, like a cord. I have some pain when rub on it.

I’m in this condition for the last five days.

Please help me understand my situation.

Sincerely,

Sky

Basically you traumatized your penis. This is a very delicate part of your body and cannot be abused by holding the blood in it like you did with the penis-ring thing for as long as you did. You will have to proceed very cautiously for the time being and not have any sex at all. If your condition does not improve you should definitely see a doctor as you could have ruptured some vital veins or bruised the veins in your penis. This is a very serious thing and should not be taken lightly if you plan on using your penis for sex in the future.

If you are having any problems voiding - definitely see your doctor ASAP.

What do you mean by "You will have to proceed very cautiously" is there anything I should do ie: cold (ice), hot compresses? Nothing at all?

At this point I think you've seriously injured your penis and nothing will help such as hot or cold compresses is concerned.

You should proceed to the doctors to see if there is anything medically that can be done for you.

Here is a link you may find useful.
(c) UrologyHealth.org - Penile Trauma