It all depends.
Receiving or not receiving the 1098-T is not the deciding factor in whether or not you can claim an education credit. Many schools have this information available directly on their websites in the finance section. The amount of your tuition and fees you paid along with the amount of student loans you took out, your scholarships and your grants. If your school does, you can get all of the information you need from there. As you walk through the education credits section of TurboTax, you would be asked if you had a 1098-T and if you don't you will say no, but you can still enter your expenses.
If your scholarships and grants are more than your tuition, books and expenses, you may not qualify for the American Opportunity Credit depending on how you allocated the grant money. For instance, if you chose to treat the grant as income and you used it for living expenses, it then becomes taxable, but you would also potentially qualify for the American Opportunity Credit.
Also, depending on how old you are, you may not qualify for an education credit. In order to qualify for an education credit, you must be 24 or older if at least one of your parents are still living.
If you do qualify for the past two years, you can always go back and Amend Your Return for the past two years.
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