Getting error message that image is too small to print

I created artwork in Illustrator in a 16 x 24 size. I want to print it this size. In order to print I saved as a JPEG.  But when I load it on sites like Society6 and RedBubble, it will only print it small (like postcard size). When I try to put on a poster, I get a message that my image size is too small.  How do I fix this? I am a newbie to Illustrator is the first thing I have created that I have tried to print.