How do I come out as lesbian to my social worker?

You can wait for a moment in which you're all relaxed and have time enough to deal with the topic, and then try to explain your feelings, tell them how you realized who you are and what it means to be like you. Try to be as honest and open as you can, make sure they know you told them about it because you trust them and you want to share this part of yourself with them. You can also encourage them to ask you questions if they have any.