Hi carlyn2,
It sounds like you're using the Messages app, but are having issues with received photos. You didn't mention if these are SMS/MMS (green) or iMessage (blue), so we'll include the settings for both.
What is the difference between iMessage and SMS/MMS? - Apple Support
iMessage uses Wi-Fi or if not available, cellular data.
MMS uses cellular data, and may also use Wi-Fi.
These two pages have more photos info for the Messages app:
Send and receive content in Messages on iPhone - Apple Support
Send photos and videos in Messages on iPhone - Apple Support
If you're still not able to view a received photo, you'll want to contact Apple Support, as they can look further into this.
Get Support
Take care!