Unusual situation, chance me for transfer?

It sounds like you are favoring Illinois Universities. I suggest you look into UIC and IIT as well if you want Mathematics or Applied Mathematics as a degree. As Faculty member at IIT, I know that we give reasonable financial aid to transfer students and UIC has tuition costs that are significantly lower than UIUC. The most important thing, however is that you find a school where you will be able to manage your mental health issues and complete your degree.