If I already input my tuition expenses into my tax forms under education, can I also include them in my work-related expenses since it is improving my job skills?

No you cannot include those expenses twice so no need to file an amendment. You can only deduct them once. If they qualify you for a education credit, then that would be more beneficial to you then a deduct. 

A credit is a direct reduction to your tax liability while a deduction just reduces your taxable income.