OK, now it makes sense.
1) EPS is good for screen printing because it is a vector format, meaning that resizing the artwork won't affect the quality. HOWEVER, the artwork must be created as vector to begin with, because just saving a regular jpeg or any other bitmap format won't do the trick. I don't recomment using PSP for this format either; for vectors Illustrator is the answer.
2) Each layer corresponds to a color. The background color usually is the t-shirt's or "whatever it is that you are printing onto"'s color. Regardless, the printing should be done in full black - another reason for saving as a vector EPS file is that you can easily change the colors without loss (in bitmaps sometimes you'll have issues with the edges).
3) If you are going to work with a bitmap image, work in a large format and save it first as .psp/.pspimage which is a lossless format and keeps the layer information intact. Only after that you should be saving to another format, i.e., saving each layer as a TIFF or BMP (lossless unlayered formats), or trying PSD, which is Photoshop's native format. DO NOT send your work in PSP's native format because most printers do not handle it as this is not a standard application.
4) Even if you do work with layers in PSP and save the image as EPS the resulting file will not contain vectors due to PSP's limitations, not to mention that the file will be flattened.
So basically, yeah, you'll have to recreate the work but doing it in a way that will actually make it possible for screen printing.