Nick here from Shopify.
You could look into using some print on demand (POD) apps for this. You could then submit your designs add your t-shirt products and then not have to worry about the shipping aspect of it all. You can find some of the most popular POD apps in the Shopify app store below:
I saw from your phone number on the site you are based in the USA. There are many different t-shirt manufacturers you could look into in the USA. I found a couple which you can see here and here. If you google searched t-shirt manufacturers and your surrounding area you are more likely to find someone local you could look to work with.
I hope this helps!
All the best, Nick