8862 has nothing to do with the American Opportunity Tax Credit. 8862 is about the earned income credit.
Form 8863 (not 8862) is not the form you receive from your school. It is the form TurboTax (TT) fills out to claim the American Opportunity Credit, as part of your tax return.
Form 1098-T is the form you get from your school, and enter into TT.
Many schools no longer mail out the 1098-T. You obtain it from your school account, on line.
To be eligible for the tuition credits, the course must be taken at "an eligible institution". That usually means, you must have received a form 1098-T, from them. But, there are exceptions. The school should be able to tell you if it is an eligible educational institution. In general, an eligible educational institution is an accredited college, university, vocational school, or other postsecondary educational institution, including accredited, public, nonprofit, and proprietary (privately-owned, profit-making) postsecondary institutions. Additionally, in order to be an eligible educational institution, the school must be eligible to participate in a student aid program administered by the Department of Education.
Enter your school at the link below, to see if it's on the dept. of education list.