Are monks allowed to have sexual relations?

No, no one is "made" to have same-sex relations.

As in any single-sex institution where celibacy is the norm, some people may resort to same-sex relations. But any use of force between people is not a skillful means toward understanding the world. Compassion for all beings is a cornerstone of Buddhist thought. Buddhist monks, just like all people, are constantly learning how to perfect that compassion, and are sometimes mistaken about what will make them happy.