this is the most important part of what you have written in the op, while this is a music theory forum, i feel my "expertise" is better addressing this than that...
take it from someone who knows, get this sorted first.
as it really wouldn't matter if you where virtuoso piano numero uno!
if youre suffering depression for example, you will think youre shit
however, doing something creative, but without the pressure of "success" can indeed be helpful for getting over mental health issues.
once you have a handle on the health issues, you will find youre more likely to have the ability to make sense of it and see your improvements, which will encourage you.
with regards to songs.
they not only give you the idea of song structure, how the scales relate to music, they also give you rhythm and timing chops, you wont get by playing scales up and down.
and at that party next summer, no girl is going home with the kid who runs through a scale perfect, theyre going home with the kid who does the rough version of radioheads creep on the out of tune acoustic they found in the corner