Hi!
I'm sorry to hear about the rough circumstances you've had in life; but proud of you for doing better now!
It's highly doubtful your old uni will re-accept you for any courses, so your best bet is definitely looking at other unis, and be honest with them about your past issues leading to you being kicked out. If you've recieved any professional help in the past, giving them evidence of this would help you prove your case (and if you aren't getting help, it's never too late to do so, it seems like a good idea even if just to show you've been working on getting better).
It might further help to ask the unis you apply to about their support services; mine were really helpful in getting me a bit of extra time with projects and being more understanding if my attendance wasn't great when I was struggling with my physical or mental health. Good luck!