I am also newly qualified in TEFL although I have been teaching for ages. I would like to teach in the Alicante area. However, I have been told that it is no good approaching the schools direct, they only go by recommendation. So your TEFL course provider should contact the schools, as if they are any good, they have built a good rapport with local schools.
Although I know some poor girls from my course were hoodwinked by the DOS. He pretended to have interviews for them but when they arrived at the school, the Head had never spoken to the DOS. However, he knew that this person was a con artist, which makes me wonder if my qualification is any good in the first place.