It feels like the inside of my wrist is on fire. Between the round bone that sticks out of ur forearm and the end of ur palm, more specifically - but concentrated at the joint. Moving my wrist in a circular motion helps to subside the sensation.
OK. This sounds to me like the consequences of ulnar deviation. Could it be that your hand is often angled to the right, particularly when you need to play with the thumb? There a myth-like old adage that says that the fingers must be aligned with the forearm to give them the most power. As a consequence, when playing with the thumb, many people angle their wrist such that the thumb is aligned with the forearm. This is not only awkward, but it leads to tendonitis in the thumb.
Another contributing factor is stretching. If you need to reach large intervals and you don't relax between playing one note and another by smoothly opening and then closing your hand, tension will build up. Example: you are sitting with the thumb on a note and need to play another one one octave higher. Reaching with the pinky an octave higher is not a trivial motion. First, most of the time, you will observe ulnar deviation, but also, the entire hand will be tensed up, and there will be a lot of stress across the palm concentrating at the base of the thumb. The trick is to release the thumb just at the right moment, before the stretch becomes too large.
Let me know if you have the feeling that any of this applies to your situation.
If Hanon will lead to injury, what method will i use to make my left and right hand of equal or similar strength. Are scales ok? I believe Chang does look down upon scales as much as Hanon - correct?
Hanon does not lead to injury; Hanon done wrong leads to injury. In principle, there is nothing wrong with doing these exercises, as long as they are done correctly. Most beginners don't have the required technique yet to do them right. It's catch 22, because Hanon is supposed to build technique, yet one must have good technique already to do Hanon.
The songs I practice are also much easier on the left hand than the right, so that method will not be too successful.
There are many threads along those lines. Check out one of the most recent ones:
https://pianoforum.net/smf/index.php/topic,5794.0.htmlI personally recommend anything by J.S. Bach. His exercise pieces are designed to build up coordination in the fingers of both hands. The recommendations by jlh are good, but if those works are too difficult for the moment, try the easier ones, particularly the Notebook for Anna Magdalena or the Klavierbuechlein fuer Friedrich Wilhelm Bach. Also, try Scarlatti. Not only will this build and improve your technique, but you will learn a lot about music and will add pieces to your repertoire. What's better than doing exercises that are musical and can actually be performed.