If you want to go for School Service then you should do a B.Ed. This will really help not only eligibility wise but also in your professional life. You can't know you can do or not until and unless you try. So you should try and in general you will get a great professional experience for your teaching as well as a chance to appear for TET.

I would recommend you to rethink about it.

I hope this answer helps you. All the very best for your future endeavors!