With a GPA of ~3.8 and LSAT of 162 (you only took it once, right?) you have a great chance of getting in to the U of A.
And yes, your "shitty" past won't ruin you. For context, I went to the U of A almost 10 years ago in undergrad and actually flunked out due to mental health issues. I took time off and then did my undergrad at MacEwan. Graduated with distinction and got 167 on the LSAT and early acceptance into law school with scholarship at U of A this year. I had the same kind of worries as you. You can also explain your circumstances in the personal statement though with your marks you'd probably get in before the holistic review anyways.