shield is considered armor therefore it shouldn't
mage armor and shield also are the same bonus type which also doesn't stack.
The Sage Advice compendium says other wise (
https://media.wizards.com/2016/downloads/DND/SA-Compendium.pdf):
"Can you use a shield with mage armor? Mage armor works with a shield. "
Also:
https://www.sageadvice.eu/2015/08/10/mundane-shield-and-mage-armor/I would say OP is correct and that AC should be 18.
