Can I add my tuition paid for a vocational school without a 1098-T form?

Probably not.  Your school must be an "eligible institution". If the school says that they don't provide that form, they are probably not an eligible institution.

 To be eligible for the tuition credits, the course must be taken at "an eligible institution". The school should be able to tell you if it is an eligible educational institution. In general, an eligible educational institution is an accredited college, university, vocational school, or other postsecondary educational institution, including accredited, public, nonprofit, and proprietary (privately-owned, profit-making) postsecondary institutions. Additionally, in order to be an eligible educational institution, the school must be eligible to participate in a student aid program administered by the Department of Education. 

Enter your school at the link below, to see if it's on the dept. of education list.

https://ope.ed.gov/dapip/#/home

If it is on the list, you qualify. After answering no to the 1098-T question, check that you qualify or an exception. That will het you to the entry screens.  Save that letter stating how much you paid for the course, in case of an IRS inquiry.