Hey, I've dealt with flat feet my whole life, and that arch ache you're describing hits home. Those stiff materials and lack of cushion can really mess with you on pavement, especially if the shoes feel narrow like you mentioned.
Maybe they're just not broken in yet. Walk around the house in them for a bit, you know? That might soften things up. And with flat feet, jogging on harder surfaces amplifies everything, so try mixing in some softer paths if you can.
Building up to that 5K is awesome, but ease into it. Short jogs first. Helps your feet adjust. Been there myself, and it made a difference.