You should check with your advisor at the school. If you want to teach,
there should be a program that combines education and art, so you get a
degree in art education. You do not need your master's to begin teaching in
Ohio, but you need to be working toward it. I don't know if you need your
masters where you will be teaching, but you could easily find out from your
college or from the local school board.
I think you might want to begin teaching first, then decide how well you
enjoy it. You can get your masters in education, or in an art area, or in
administration, in case you want to move up in the system.
Hope this helps.