I like the imagery and the idea. I would avoid phrases like "for I" because it sounds pretentious and very unnatural. Instead, opt for a more casual voice, because then you connect with your readers more. You talk to them, instead of "at" them, if that makes any sense. For example, say "because I want to live under the sea" instead of "for I want to live under the sea."
Better yet you could say "Because I yearn to live under the ocean." It is just a subtle change, but the different word choices creates more interest I think.
I'd also watch out for the use of tenses. Instead of saying "admire how slow I can move and be at ease" you could easily reword it to "Admire how slowly I move and my ease". See how you can rearrange little things to make it more "flowy". By cutting out the word "can", the sentence flows a little easier.
I did a quick full edit, if you are interested.
I envy Ariel,
Because want to live under the ocean and
Have the fish and their bubbles as friends,
I want to feel my hair dance through water,
Admire how slowly I move and my ease.
Imagine the different colors and creatures I'd see,
But in the end, I'd surely be alone,
because thoughts and my dreams would be my only friends
I don't usually do a full edit but I think your poem is very beautiful, it just needed to be polished up a bit here and there, which is easier to do from far away when it isn't your own piece. Me and my friends do this for each other, edit each others work, because they have a perspective I don't.
Also, in the future, read the poem out loud to hear how it sounds, sentence to sentence. You don't want it to sound choppy or blunt, but smooth and flowing from one verse to the next. Good luck and good job!