If a school I attend and pay for is not a title IV institution, can I still claim it and get a tax break?

Here is a link to a database of schools that are eligible to use for education credits.

No.

 To be eligible for the tuition credits or tuition & fees deduction, 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. If they issue a 1098-T they are probably an eligible institution.

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

https://fafsa.ed.gov/FAFSA/app/schoolSearch?locale=en_EN