I read it so I could give an opinion.

Firstly as a writer myself, I'm not gonna be the one to discourage you. If you like writing and specifically like writing fan fiction, then keep at it. There's always room to improve.
If it's an idea you like and want to run with it than go with it. When writing fan fiction, you're using characters that are already well known. They have a personality and a story that's already been set by writers, so there's a limit in a way because whatever the story is about, you need to make sure it's believable to what the characters would do. Personally, I'm not a fan of Anna and Elsa, but I think they would read the bottle before drinking it. Though I find it believable that Anna would want to pull a harmless prank on her sister given the chance, I think she would be more concerned about her invisibility.

It's also good to realize that there are more ways to say "said". Having "said" be your only way of how people talk make everything they say seem very monotone and without emotion. Check out the link I posted below. Questioned, yelled, exclaimed, cried, joked, etc are just a few ways to express not just what a character says but how they say it. The link I posted below offers 100 different example to find the perfect word. These words typically go after the character's quote. Also, when a character speaks, that begins a new paragraph.

link

Fan fiction gives you a chance to take creative licences on the characters and stories, but believability to any story is key, even with fantasy. There always needs to be a sense of logic. Such as Frozen. Of course we don't believe in ice powers, rock trolls, or talking snowmen, but Disney creates a believable universe in which we believe and accept it as true and we're even entertained by it.

Finally, I'm not too comfortable with Anna and Elsa falling on each other naked by accident. I don't know, to me, it's weird. But that matters too. If you're happy with your story, go with out no matter if anyone understands or likes it or not. If writing is something you like and want to do, than keep going.