The face is the most obvious part of our body, so it is not surprising that so many of our expressions and idioms should feature parts of the face. As you read through the ones that follow, try to picture the face of someone you know well. If you attach each of these expressions to the features of that person's face, then it will help you to remember each phrase.
Let us start with the eyes. If you are up to your eyes in something, then it means that you are fully occupied with that thing. You might tell a friend, I can't come out with you tonight - I'm up to my eyes in homework. This means that you do not have a free moment because your work is taking all your time. You can remember this phrase by thinking of yourself surrounded by piles of books which are so tall that you can only just see over the top with your eyes.
On the other hand, if you only have half an eye on something, you are not giving it your full attention. It means you only give something a quick glance. I only had half an eye on the television because I was supposed to be doing my homework. Think of half an eyeball sitting on top of the television set as a way of remembering this phrase! The phrase with your eyes open is used in a figurative rather than a literal sense. For example, He is working really long hours in his new job, but he knew that would be expected when he took it on: he went into it with his eyes open. In other words, he knew all the facts and was not deceived. It means that he was fully aware of all the circumstances.
If you want a phrase which means literally that you watch something carefully, then use the phrase, keep your eyes skinned. This does not mean literally that you 'skin' - remove the skin off your eyeballs! It means that you do not allow anything to stand in the way of your sight; you see clearly and sharply. Keep your eyes skinned, officer - there may be robbers about.
Facial idioms mention the nose as well as the eyes. To keep your nose clean has nothing to do with the careful use of a handkerchief! It means that you avoid trouble or the taking of risks. If you keep your nose clean, you have a good chance of being elected class monitor.
Think of someone with a big nose that you can see clearly to help you remember the idiom, It's as plain as the nose on your face. You can see someone's nose very easily and clear ly; this idiom makes reference to the fact in showing that something is easy to see. Similarly, something which is under your nose is very obvious and cannot be missed. I can't understand why you couldn't find your shirt - it was on your bed, right under your nose.