I'm having trouble with Gimp dpi ( they keep comming out pixelated on tshirt websites

[orlandodc2]

ello all,  I recently got into the t-shirt design hobby/business.  I downloaded gimp and have been using it to turn my hand drawn art into computer based art for Tee Spring, Society6 and many more.  The issue I'm having is that for some reason my lines (mainly the curved lines look pixelated.)  after seeing many videos on how to change the DPI on gimp I keep only seeing how to only change PPI. 

I did notice that to change the PPI it automatically changes the art design to smaller dimensions is that why I get's pixelated because its being stretched on the t-shirt?  What is also weird is that when I make the art larger to where it bleeds out of the printing zone the pixels seem to be more smooth.  (the following pictures are for examples only and not the actual design)

so my questions are:
Can I create art on gimp for t-shirts that will be printed on Society6,Tee Spring, Red Bubble etc.?  If so can someone please give me detailed instructions how to fix the issue or maybe even a video link to one.
Thank you for your time.

[Blighty]

(Photobucket images not showing)

Gimp (and all bitmap editors) work in pixels. It is better to think in pixels.

For example:

a 1200 x 1200 pixel image @ 300 dpi will print 4" x 4" (1200/300 = 4)

a 1200 x 1200 pixel image @ 100 dpi will print 12" x 12"

if an image is to be 10" x 10" @ 200dpi, then 2000 x 2000 pixels is required.