Sounds like you are doing the designs fully in Illustrator. The more efficient way would be to do the designs in InDesign and import the artwork. That way when you update the original source image, everything linked to it will update automatically.
It is possible to link a file in Illustrator as well. Not sure that it works if the original is in Illustrator format, but at least if you save as PDF or EPS, you can import the file
linked rather than embedded to the same effect.
https://helpx.adobe.com/illustrator/using/importing-artwork-files.html
Kalleheikki Kannisto
Senior Graphic Designer