Be forewarned: cynical/grumpy late-night posting follows.
My concern is that the admissions committee won't see it that way and will say to themselves "well if that's what happened to this kid going from highschool to university, imagine how he'll adjust to law school"
They won't think that.
What they WILL think, after reading the first couple of sentences in your personal-statement-that-resembles-your-post is "oh look, another applicant with a sob story about how depressed he was during college. NEXT!"
Heck, I couldn't even read it all myself. I started skimming at "depress..."
Honestly, even though it was obviously unique and horrible from your perspective, versions of this story show up in a whole bunch of applications - not surprising, because a whole bunch of people had similar issues. Sure, your situation might have been more extreme than most, but "srsly d00ds, I was WAY sadder than those other guys" is not only not convincing, but almost as standard as the underlying sob story.
This approach will not serve you well - not because it is too personal, but because it is too common and boring, and - perhaps more importantly - because it amounts to an excuse, despite your protestations to the contrary. And if there is one thing lawyers (including law professors) dislike, it is excuses.
Or, as my old boss used to say: "No whining!"
Anything that has even a whiff of "woe is me" is a huge negative. Don't do it.
Instead, own your screw-ups and turn them to your advantage. The last part of your post starts to do this. It didn't kill you; it made you stronger. Summarize your travails as briefly as possible ("I faced some personal challenges during the first year of college that adversely affected my grades"), just enough to set up the powerhouse part of your statement, where you can talk about how a stint in the psych ward makes you uniquely prepared for the practice of law. But make it positive, and no whining. Admit that your GPA is bad, and there is nobody to blame but yourself - but suggest that your GPA perhaps does not fairly represent your capabilities, as shown by your 178 LSAT score. (Because the best way to prove your point is by kicking the LSAT's ass. So make damn sure you do really well on the LSAT.)
Law schools look for discipline, initiative and leadership. Show them some.
(And then keep that personal statement handy for bar admission, when you will most likely have to discuss being committed.)