Dear Princess:
If you are one in a million, you are able to learn correctly to play without a teacher. However, taken for granted that's not the case, you must have one. The basic problem is that you probably don't know yet how the things might sound, and thus, it's impossible to explore the piano to find out how to get there.
Anyway, if this someone that helps you gives you some actually good advice, it's better than nothing, since you follow this strictly. Another problem: in the begginings, you have so many things to consider that something always is beyond your control. In that sense, let me please advice you about the steps of good practice, in my humble opinion:
- first of all, think of fluency, that is, you have to play the correct note at the correct time with the correct finger. Then, you shall consider your movements, your fingers-hand-forearm-arm-shoulder position and "stiffnessless" (actually, you have to feel your muscles at work);
- the second step is touch and sound. Here is a main problem if you don't have neither a huge musical background nor a teacher, because you must know what is the music musically speaking. This is a very neglected part, and a most important one, because it's when you will shape your very "piano voice", so to speak;
- third: power! The strenght and the control of it: the possibility of break some glass with your sound.

In the other hand, the possibility of playing as soft as a whisper. Here we have a serious concern: heavy playing + wrong technique = injury!
- last-but-not-least-but-last: speed. Yeap... sometime you have to consider it. The piano repertoire have lots of music that requires fast scales, very fast arpeggi, ridiculous fast octaves, and so on. Again, fast playing and wrong technique are fatal to your muscular apparatus.
So, I hope that brief consideration shall help you a bit. In my most sincere opinion, I think you can play without a teacher but don't expect nor try to hurry in your progress: take a piece, play it for your leisure, think about what your friend says, take in account what people write in the forum. Specially, don't play fast or loud yet. And as soon as possible, get a regular teacher!
Best to you, and Happy New Year!