Hello Hikky,
Hopefully I can offer some suggestions as well as criticisms regarding your situation. First of all, on the issue of money, there are other options that allow you to take lessons at a reduced rate. For a year before I went to university, I took my piano lessons at an music/art school that was geared for the community (not like a conservatory or anything). You could sign up for your instrument at any level and get placed with a teacher. When I did this, I went to the school for an interview in which we discussed my plans for piano and what I would like to get out of a teacher. After that, I was paired up with a teacher who I still talk to now. Granted I have a new teacher at the university conservatory, but every time I am back at home, I always visit and find her advice quite useful.
But for money, music schools like these also offer financial aid programs for students who may not necessarily be able to afford lessons in full. If I can recall correctly, the starting rate to begin with was something like $62-$64 per hour, and from that point, depending on your financial situation, you could get that rate appropriately reduced.
Now on another note. After a while I kept my teacher, but no longer worked financially through the music school. I would go to her house / studio close to the music school and take lessons only through her. There I learned that she offered a reduced rate specifically for college / near college students. Then I only had to pay $50 per hour. Small options like these are ones to consider. Teachers are people too, and some of them may cut you a bit of a break. I know that $50 is not cheap, but it also not ridiculous either. There is some truth in price of lessons, but that is also only to a degree.
I had a teacher when I was younger who gave hour lessons for $30, and she ended up being a bit loose in her teachings. That would be somewhat of an example of a teacher equivalent to her rates. But, hell, I remember my first teacher charged only $5 for a weekly half hour lesson. He was almost 90 years old, sharp as a whip, and asked for so little because he was no longer in it for the money. I wouldn't recommend this option as you get better, but for a beginner teacher he taught me a good amount of useful tools and techniques.
Okay so about the problem you see with being a self taught individual and problems you may have with a teacher in general. I would say that piano is already a drastically individual and solitary activity to begin with. I take hour lessons once a week, and other than that, I am practicing for hours by myself. You also talked about the issue of being nervous in from of your teacher. I remember being the same way, but you get used to it. You actually need to get used to it, or else the whole aspect of performing in from of one person, never mind a small/large audience will go out the window. The teacher is there for all the reasons people have stated in earlier posts. But the teacher is also a perfect guide. They will know the progress you have made, and when the right time will come when you have successfully learned a new technique, or successfully learned a piece to a good extent. A teacher will also offer you performance opportunities, ones that help another drastic component of playing- performing in front of others.
I understand where you are coming from though. I too tend to travel the path of self teaching. I like studying things on my own. In fact, I am also learning Japanese right now. I am taking classes, but because I will be studying abroad this summer, I am taking that extra step to learn other useful things that will benefit me while I'm there.
Oh and about you video that you posted. I know you asked what kind of things were noticeable in your performance. Well, I first noticed that you are playing very lightly. One important technique that is important especially in virtuosic playing is a firmness and tightness in your fingers (not wrists!). This will convey confidence in your playing, and produce a much better tone. You also have a bit of a flaring pinkie, but that should diminish with time I would think. Also, while I couldn't tell completely from the camera angle, it looked as though your left elbow was doing a sort of "out an away" motion- something that I actually had a problem with for a little while. When people lift their hand away from the keyboard, they tend to swing the elbow outward in what they think feels like a lift, but is really just a simulation / sensation of one. Try to be cautious of that.
I think that you are progressing quite nicely. One last thing to note as well. While these initial stages of learning may feel comfortable and fun, there will be a point where you may feel you have reached an upper bound. That is where the teacher really is necessary. They will help you to pass that bound and help you to raise the bar more. In fact, that teacher who charged $30 and hour got me to my limit with her, and then I realized that she really wasn't as great as I initially thought, because she couldn't help me progress anymore.
Wow that was long, hope that at least some of it was useful.
Ryan