I like the theme and a lot of your mechanics a lot, you have some good stuff here. But....it honestly feels like you have two subclasses here instead of 1.
The fact that you can cast a spell higher than is normally possible is a BIG deal. Its cool, its unique, its special.... and its the foundation of an entire subclass, that's how good it is. You then add a lot of top of it, which is out of scope for what a sorcerer orgin should provide. I do like the 6th level abilities, I think you have the makings of a fun force sorceror type subclass in there....but it should be its own thing.
Also on the charges. The charges are a cool mechanic but they scale out of control in the mid to high levels. To give you my best example, at 18th level, if your character decided to "win the game", they could focus all of their energy and cast 10 9th level spells in a single day. That would already be too good....except you get to cast all of your normal spells too.
So unfortunately we have some work to do.
My recommendation:
1) 1st level ability: 1/long rest to recover sorcerer points equal to half your prof bonus (round up), which triggers arcane damage equal to 1d4 per sorceror level (with your save to negate). We are starting your charge concept but in a way that is weaker but more generally useful. Also note I used a recovery not a simple gain, this is to prevent a morning charge up, heal....and then nova later in the day.
Also I would remove the area effect of your arcane discharge. The wild sorc is already annoying to the party enough with its area effects, if you want to take damage for power by all means, but don't force your party members to have to suffer it to.
2) At 6th level we give them the bound spell. Its usuable 1/long rest, and costs sorceror points = spell level. If you want, you could provide the option of taking 1d4 damage per spell level instead of the sorc point cost (no save, they just take the pain).
3) I think arcane body is fine at 14th except for the arms power, which is weak compared to everything else.
4) For the 18th level, I really like the form idea....but again looking at the power scaling we are already providing (an extra 9th level spell at this point, something no other class in the game gets), this can't be too much. Maybe you let them select 2 bound spells, or an extra sorc point with their 1st level ability... something nice but nothing too strong. You already providing the meat with your extra 9th level spell, so this is just as a little desert to enjoy.
And then if you wanted to go with your current 6th level abilities as its often subclass (effectively gaining "metamagics" that let you morph your sorceror points into various forms), than go for it! I'd be interested to see what you came up with there.
