Yes I guess it is very difficult to find a teaching position unless you are native in English.
You'd be surprised! Though for non-native non-Poles the main possibilities (in Warsaw anyway) are either doing the Callan Method or being very lucky and finding a real language school who are looking for teachers but can't find enough (often due to all their clients wanting lessons at the same time of day).
If you're also looking at places other than Poland, why not Saudi Arabia? The work usually pays quite well and female teachers are always in demand due to the large number of female students - there are plenty of Turkish people teaching English there, and if you are Muslim, this is a definite advantage too.