Is there a way to enter education expenses manually?

The TurboTax online editions do not have direct access to any forms, schedules or worksheets.  That option is only available using the TurboTax desktop CD/Download editions.

Yes, enter any expenses you paid, either out-of-pocket, with credit cards, or with student loans.

In the Deductions & Credits section, scroll down to the Education topic and go through the interview questions carefully.  The section is titled 'Expenses and Scholarships, Form 1098-T', but you will enter your expenses there also. 

First, you will add yourself as a Student, then give info about your school, then enter your expenses.  You don't need a 1098-T to do this if you did not receive one. 

Here's more info on Qualified Education Expenses and Education Credits to help you.