Vishal, I wrote once responding to another poster, but haven't responded to your post.
I've been learning the piano for 2 years (mostly on my own, and under a teacher for 6 months).
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I believe more in self-learning, rather than learning from a teacher. This is what works better for me. ....
I was a self-learner, and this was not by choice. When I was young I was given a little air blown organ (1960's), then a piano. I was given a book meant for self-teaching adults - I found the book recently so now I know what it was - and later books my grandmother had used - these were intermediate level sonatinas and a book of Czerny etudes, all of it published around 1910 and used in a conservatory in Bayreuth. I played up a storm in my own manner. Decades later my mother told me that I had a "crude and rough" way of playing. Then I had no piano for 35 years. Then lessons on another instrument, where I got to understand about technique. My self-teaching time lasted from age 8 to 18.
I got a piano again several decades later. At first I could not get a teacher and chafed at that. I tried to rectify my playing as well as I could from what I could find via the net, and refrained from playing much, esp. harder things, until I could find that teacher. The one thing I did "learn" (scales, by Cooke) is the thing that we've had a right time trying to undo the damage of. What you read, what you understand that you read, and what you understand your body to be doing vis a vis this, any or all of this can be off.
So I know a little bit about the self-teaching side.

I will say that I also learned many things from it - not to make it all black and white.
I have been working with a teacher for quite a while. First point:
any teacher is not good or better than self-teaching; a poorish or mediocre one may be worse than going it alone.
When it comes to doing what "feels relaxed" or "without undue tension" - when you are guided into this, you will realize for the first time what this is, and until you have experienced it, whatever you are doing presently will feel correct to you, because it's the only experience you know. Another thing is that the teacher will see things you don't see, from unexpected places you would never think to look, and if you go with what is suggested. I have a great deal of independence with my teacher: a great deal of self-observation and responsibility for myself - and given the mess that has to be undone, it is even necessary.
The only way to be able to form true opinion of what is best for our learning in regards to (good) teacher or not, is by having experienced both sides. The "good" part is important.
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In regards to observations of your playing. As a learner myself, I am not qualified but I will offer some general impressions, gut feelings if you will. I suspect that your body is not working as a unit, the fingers are doing a lot of the work, and that you are holding the non-playing fingers "out of the way" which creates the tension we see. If so, things you do with the fingers will feed back tension into the wrists, arms, or neck. These are things I have had to work through myself so I may be extrapolating. Knowing that the body works together, that what happens in the fingers happens along the entire system, and being able to work with that idea, are two separate things. Personally I have needed feedback and a back and forth, because I cannot see what I can't see, or understand what I can't yet understand. That is, after several years I can start understanding what I see in videos of people playing, or on-line lessons and demos (including the bs) but can still be caught out.
Best of luck to you. It takes courage to post a video like you did, and you have worked hard.