I think you can get quite far on your own, but there is one thing that is important to learn correctly early on: how to move your hands across the keyboard. It will be easy to get right now, but very hard to fix later when you have to basically unlearn a bunch of stuff. I'd recommend taking a few lessons for this, but if you want to try for yourself:
Start with the thumb of your right hand on the central C and your right hand fingers on the four subsequent tones (D, E, F, G). Your fingers should arch graciously on the keyboard. From this position, we'll start playing the C scale by first pressing down C (thumb), D (index finger), E (middle finger) and then you move your thumb underneath your fingers to the F key and press down. Next, your fingers move up to G (index), A (middle), B (ring), C (pink) and then you continue the scale by pressing those keys one by one. This is how you move up the on the keyboard.
Going down, you start with your pink on C' (that is one octave above the central C, exactly where your pink ended in the previous exercise). The sequence now is C' (pink), B (ring), A (middle), G (index), F (thumb). At this point your middle finger moves over your thumb to the E and presses down. Then your index finger presses down D and finally your thumb lands back on C. This is how you move down on the keyboard.
Once you can do this smoothly within the octave, you can extend the sequence to cover the whole keyboard. For your left hand, you have to mirror this (PM me if you need explanation).
You don't have to learn this technique, but if you don't, you'll create a glass ceiling for yourself. Some music will simply be unplayable if you cannot do this properly.
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