How to print photos through my iPhone?

My printer has its own Wi-Fi but no connection to the Internet and I'm confused because when I print it doesn't pop up as a air printer

If your printer is not airprint compatible then go to the app store and see if the is an app from the printer manufacturer
As you don't say what make or model of printer you have that's the best we can do
HTH

Yes, printer Wi-Fi connections of course are not internet accessible ones. AirPrint only works with select printers, most of which are detailed on Apple's website.

If your own isn't one of these then there's likely software available to be able to connect to that wireless network in order to print from it. HP for example has that.