Is it grammatically correct if I omit "you're" from "you're just a ringing in my ear"?

What's "messed up" mean here?

Here, "messed up" means to have made a mistake or done something to get in trouble. Ex: He messed up the whole project. Ex: She messed up when she forgot to lock up the store. Ex: Try not to mess up again.

Isn't it right to say "on the album" not "in the album"?

In this context, it is correct to say "in the album", because "album" here is referring to a photo album. A photo album is a book filled with pictures, and the pictures go "inside" the album. Therefore, it is more correct to say "in the album" in this case.

In this case, could we think it means "write a letter" even though it didn't designate that it's about letter?

Yes! :) When Allie is saying "Why didn't you write me?", she is definitely referring to a letter even though she didn't specifically say it was a letter. Another example of this could be: "He wrote to me last week about his experiences at university." In this example sentence, the man wrote a letter to the subject. Usually in English, if it's by email or a text message, we will say it was by email or text message.

Is it grammatically correct if I omit "you're" from "you're just a ringing in my ear"?

Yes! You could definitely omit the second "you're" in "you're just a ringing in my ear" since it comes after "You're not a voice." The subject has already been mentioned the first time. This actually sounds more natural within conversation. I'd say the second "you're" is mainly for emphasis here. So depending on the context, the "you're" can be effective for that. Ex: You're not a voice, just a ringing in my ear. Ex: You're not Santa, just a man wearing a red suit.

Doesn't "rip" mean "tear something"? What does "rip" mean here?

Yes, that's correct. Conventionally, "rip" means to "tear." The speaker has used it here to emphasize the force or violence with which the driver has pulled on the brakes. He does not mean "rip" in the normal sense, as in the racecar driving circle, "rip the brakes" is an expression used to mean to pull the hand brake to slide around a corner, thus causing the car to drift or slide to a stop. Ex: There's a corner up ahead! Rip the hand brake. Ex: I accidentally ripped my jeans.