Where it says Veteran's Education Benefits do I need to enter the amount it says on the 1095-T form under Payments received for qualified tuition and related expenses

No, the Payments received for qualified tuition and related expenses are the charges the school received for classes and other expenses.  Your veteran's education expenses should be included in Box 5 (Scholarships) if they were paid directly to the school.  If they are not included there, you can check with the VA (See View your VA payment history).