My friend recently did one, she shared it on Instagram, Facebook, & Twitter. Her post was basically just like the photo on Facebook and comment that you liked it. After the month was over she tallied up the people, picked one at random, posted the winners name on Facebook, Twitter, & Instagram and the person just privately messaged her the address for shipping.
She is not business savy at all so did not know of any legal requirements, likewise restrictions and got away with it. Not saying you should do anything illegal, but unless you are like a huge company and (have value to lose) I don't think Facebook is actively seeking to call you out. You know?
It looks as if you got everything figured out and have the give away posted! Good luck and much success, I wouldn't worry either :)