The impression that I got was that these TESOL courses were a waste of time and money. To tell the truth it was interesting and I learnt something about English grammar but there is no legal requirement to complete a TESOL certificate before starting to look for work. Tesol or CELTA do not lead to QTS (qualified teacher status) and holding a university degree is by far the better option, especially if you want to travel further on such as South Korea, after gaining experience, where a degree is compulsory. In a Trinity or CELTA course you will be expected to complete the equivalent of six hours of monitored teaching but what is that? You will get more than that after your first real day of teaching in a classroom anyway. My course cost £520 but that was in 1999/2000 so probably costs much more now. The trouble is that schools will probably want experience of teaching in their methodology, i.e. the Callan Method and you would be expected to know the syllabus for First Certificate and maybe business English. These things will not be gleaned from a CELTA course, only the three P's.
require both CELTA and a university degree. You'll have to check this out yourself.
Many years ago, I was in Poland in a place called Krasnik and local schools were even employing young Russian girls from the Ukraine to fill the huge gaps in the shortages. I would think that they would take any native speaker with open arms.