Can you file without your schools 1098T form?

You should not. You want to make sure you are claiming what the form says. Check the bursar account to see if it is available.

The 1098-T is only an informational document. You claim the tuition credit, or report scholarship income, based on your own financial records, not the 1098-T. 

If you claim the tuition credit, you do need to report that you got one or that you qualify for an exception (the TurboTax interview will handle this)

The 1098-T is only an informational document. The numbers on it are not required to be entered onto your tax return. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or deduction or possibly your student has taxable scholarship income. 

If you claim the tuition credit, you do need to report that you got one or that you qualify for an exception (the TurboTax interview will handle this)

In the 1098-T screen, there's a link "What if this is not what I paid the school" underneath box 1, where you can enter the actual amounts paid.