Is it possible to teach English without a TESL certificate?
Yes, but you'd have to either work for an exploitative cowboy outfit or go it alone, legally or illegally.
I have EU citizenship
That would be a big help.
I have a Maste's degree in Library
I'm not sure what an MA in Library
means, but an MA means a lot here.
Would teaching English cover average living expenses?
It covers more than just living expenses if you are qualified. Why not take a course in TEFL/TESOL? The outlay would make a big difference in the long run.