Karlie here from the Shopify Support Team! It sounds like you're interested in having a print-on-demand type of online business. Print-on-demand would allow you to upload designs to an app and have the app print out the designs on apparel and ship the finished product out for you. There are quite a few print-on-demand companies that you can find through the Shopify App Store. Specifically I would recommend checking out; Printful, Printify, and Teelaunch. There is also a really great guide that you can check out to help you start your print-on-demand business, you can check out our free video tutorial, here.
If you want a way for customers to be able to upload their own images so you can print them on products, then you would want to look into an app. You can check out the apps; Custom Product Builder, Best Custom Product Options, and Personalized Image Uploader.
I hope this has answered your question. If not, or if you have any further questions please let me know. I will be happy to help!