Ok, Galadriel shall then remain in Doriath for a while and get more acquainted with the everyday life of the realm. She will finally reveal the atrocities of Alqualondë when she feels ready to do it, even though Melian will get closer and closer to the truth as she explores deeply the depths of Galadriel's mind. If I'm not wrong, it's exactly Melian who 'convinces' her to get rid of that heavy burden.
As it's narrated in the Silmarillion, Galadriel nonetheless tells the Maia a part of the real state of things: the terrible end of the Noon of Valinor and the theft of the Silmarils. What Fëanor committed is unveiled, as you wrote, later and it so becomes the cause of the Sindar's hostility towards the Houses of Fëanor and Fingolfin.
Another aspect. When is Galadriel to meet the love of her life? Should Celeborn appear in the story, in your opinion, before or after the suffered confession of the Princess? Honestly, I would have her begin to interact with him once she's freed from the sorrows and guilt (though not directly responsible) of the Kinslaying. What do you think?