Me, personally, I would have to give up a few activities and take up other ones, but not too many. Most things we do can be done one-handed, nowadays, typing, driving, operating most machines. This includes getting married and all that that implies.
Sure, it's a handicap, but at least it's not a mental one. You still have your mind to find solutions, and you are far better off than a lot of people.
What is your problem with getting married without a left arm? The wedding ring doesn't have to go on the left hand. It doesn't seem like a deal breaker to me. There are a lot more important things to consider when choosing a mate than the number of limbs they have, like their personality and strength of character.