Even in this brief question, you sound like a survivor who has already overcome obstacles that many of your contemporaries have not encountered. And although, sure, there will be some admission folks who could be wary of accepting a student who might come with risks, there will be others (probably more) who will respect your candor about your past struggles and your efforts to move forward, and who will embrace the opportunity to assist you on your journey. The fact that you've already excelled in classes at a community college and, above all, at the university you're hoping to attend, will work strongly in your favor.
When you apply, you need to disclose your past (and all the bad grades you earned at your first school) and the measures you've taken to move forward. It would also be helpful for you to submit a letter from a current or recent therapist that attests to your readiness to take on full-time college life. Most colleges these days (even the biggest public universities) evaluate their applicants "holistically." This means that they examine the whole student ... not just the GPA and test scores. So you need to submit an application that explains the mental health issues you've dealt with and what you've learned so far that will allow you to start school again on firmer footing.
You can tell your story in your primary college essay, in the "Additional Information" section of your application (if there is one) or in a supplemental, unsolicited letter or essay. In situations like yours, "The Dean" often recommends using "Additional Information" or an extra essay for this disclosure, saving the main essay for an unrelated topic. This sends a message that suggests, "Yes, I've had these problems but they don't define me." On the other hand, the essay prompt on transfer applications is commonly something along the lines of "Why do you want to transfer?" And thus this is an apt place to tell all.
Although it sounds like you're aiming for one university in particular, it would be worthwhile to pick out a couple additional choices. As noted above, most admission officials will be in your corner when they learn about the steps you've taken to get back on your feet, but — because your path so far has not been a straight line — it's possible that you'll get unlucky and the subjective nature of the "holistic" review could work against you. Even if you don't get good news from your top-choice university (and I suspect that you will), there will be many other schools that should welcome you.
As "The Dean" has said often before, College Confidential is a terrific place to get valuable (and free!) information about the college admissions process — including answers to questions that you can't find elsewhere. But never believe EVERYTHING you read online!
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