How do I cast iPhone photos to TV without Apple TV?

You need a TV which is AirPlay 2 capable or you can connect your phone to your TV using a HDMI cable. Most modern smart TV's are AirPlay 2 capable. Check the manual for your TV to see if it is AirPlay 2 capable.

you will need one of the following

1. an apple tv box
2. a tv that support airplay Apple TV app - Devices - Apple (EG) scroll down to section "AirPlay 2-Enabled TVs" this list is unlikely to be up to date
3. a tv that support chromecast or a cromecast device connected to the tv and then you get some of the chromecast apps in app store
4. a tv that support miracast and get some miracast app in app store
5. an app from the manufactorer of the tv that support their own way of doing it
6. an <connector of your phone> adaptor to HDMI

Lightning Digital AV Adapter - Lightning to HDMI - Apple or Belkin Connect USB-C to HDMI Adapter - Apple

just because apple make their airplay std that do not mean all tv manufactorers adopt the std. heck they probably has to pay license fees to do so.

AirPlay-enabled TVs will have a setting to activate it, that may be off by default. Try finding a setting for that.

What is your model TV, and its year of introduction for that model?

If the TV has the service and both devices are on the same WiFi network it can be done without Apple TV. But if the TV lacks the capability or doesn’t connect to internet it won’t work.