The Bible does not ask any more of you in dealing with homosexual temptation than it does of someone in dealing with heterosexual temptation. Those who are heterosexually tempted have marriage as a way to deal with temptation. No, marriage is not God's way to satisfy lust. Genital sex is neither a right nor a necessity. Wanting to enjoy another person's beautiful body is not sufficient grounds for marriage.
Sexual response has non-sexual roots.
I know that you are angry at the way God made you. Consider King David's response when he reflected on how God created him. Perhaps you are envious because of others who are better looking, or who are more socially at ease, or who do not seem to have a problem with sexual temptation. The grass always seems greener on the other side of the fence. Because a cannibal eats his enemies to possess their good qualities.