What's the Name of That Book??? discussion

Honestly, I read this book last year but I CANT seem to remember it! :( It was about this society where there's no pain and I think that the children are created to be perfect(?) It is NOT The Giver. In the beginning of the book I remember that a guy (the society's leader's son?) has taken a major liking to the main character but she doesn't like him and I think she hits him. After that, he basically puts her in danger by taking her to some room. He and his buddies then decide to create a fire and pretend to be savages when suddenly a REAL savage shows up. I forgot what happens afterwards, but the girl ends up in a situation where she is camping with that savage in caves and such. She even starts her first period with him by her side and he said that she smelled like violets? I don't know if that helps but PLEASE help!!! Thank you. Oh by the way, the society lives in a dome and there are different rooms like recreational, theatre, etc. I'm not for sure on this but I am pretty sure that the society is equal and that (for i.e) even if you're winning a game, in the end you still have to make it a tie. (like I said, I am not sure on this point!)

Title: Under The Never Sky
I was trying to search up another book, and coincidentally they both have the word "sky" in them!