My understanding is it means someone has no choice about doing something, or that something is not optional, for example 你非去不可 you must go 对，你理解的没有问题！ And it can also be used in a situation in which you make up your mind to do something. for example, 我要努力学习 下次考试非拿第一不可.Or 西藏实在太美了 今年夏天我非去不可. Could I use it in this way 我努力不爱上你，但我非爱你不可。 I think the most idiomatic way of saying this would be "我努力不爱上你，但我做不到。"

You are correct.

非 = 不. This structure is a double negative. So they cancel each other. 可 in this case means "must". So your understanding is correct. 我非爱你不可 = I must love you. Your translation of "I tried not to love you, but I have no choice in the matter" did not have the same nuance in English. "我曾试不想爱你, 但我沒有选择" Your version is "I strive not to love you but I must [love you]"