I wonder what percentage of the world's texts contain photos of family pets. In any case if you can't see the notification one option of course is to pull down from the top edge of your phone and that should show you all the recent notifications.
If it's no longer there you need to open the messages app and look there. Now the messages app should be easy to find on your phone, but if it's buried somewhere it may have gone to a different screen than the first home screen. So you can swipe to the right or to the left to look at other screens until you find the messages app.
If you still can't find it you should be able to use Spotlight search to locate the app. To do that swipe down on your home screen not from the top edge, but sort of from the middle. That brings up Spotlight search type messages or just the first few letters of messages and it should locate the app for you.
You might make note if it's inside a folder because you can put apps inside folders and the name of the folder will appear in the spotlight search results. Then you'll know for next time where the app is. In the case using Spotlight search you can tap on the icon and open the messages app to look at the lovely photo of your family dog.