Do you want to teach English in England or abroad? Some countries only require for teachers to be English natives but more and more will ask for a CELTA or TEFL.
Here are the conditions to enrol on a CELTA course and I believe the same apply to TESOL
have a standard of education equivalent to that required for entry into higher education
be aged 20 or over
have a standard of English which will enable you to teach at a range of levels
I've just finished my CELTA and it was hard work but trully enjoyable.
You should be okay without a degree, however I strongly suggest that you revise your grammar for the entry test, also the 4 written assignments have to be in an academic style, which some of my colleagues struggled with but it is not impssible.
Good luck!