Ok, this is finally starting to make sense. I'm sure it was a simple miscommunication but what they need is your design on a transparent background and JPEG doesn't support transparency. Vector files are more universal than PSD files so that usually simplifies the process. Depending on your design, it may vectorize quite nicely. If not, and you created it in Photoshop and still have your layers intact, just get an image of a blank t-shirt on the web and put in on the bottom layer. Then knock out everything that isn't t-shirt on your design. That will give you an idea of what it will look like and you can make adjustments. When you're satisfied, delete or hide the blank t-shirt layer and then export it as a PDF. That will preserve your transparency, with the proper settings. 'High Quality Print' preset should be good. You could also export it as a TIFF or even a PNG, which any decent print shop can easily deal with, as long as the resolution is exactly scaled at or above 100%. Does that make more sense?
If you need some advice regarding your design, just post a screenshot or image here.