@persia501,
Well - you should understand that one of the definitions of insanity is the inability to tell the difference between fantasy and reality.
Also, at age 19, your hormones are talking. LOUDLY. I recognize it is not easy to ignore them but, what you are saying that you cannot be together anyway. So you're torturing yourself with these thoughts.
Can you both leave the country? Is that even an option? The way I see it, your choices are -
* Ignore this and go on with your lives. Break up (or not) with your current girlfriend. Your cousin does whatever. So be it.
* Leave the country, both of you, and make a go of it. This way is expensive and difficult and there are no guarantees.
* Have an affair, whether you stay with your girlfriend and your cousin stays with her boyfriend, or not. This way has secrecy and lies attached to it. Your family is very likely not going to be happy with it. And your girlfriend and your cousin's boyfriend are of course going to be badly hurt by it. Because, inevitably, someone will slip and you will be found out.
* Be together, and be open about it. And be prepared for, perhaps, a lot of disapproval, from your family, etc.
Sorry this is harsh, but you need to make up your mind about these choices, or find some other choice I haven't listed. Pick your poison.