Photos section is grouped by Moments that are relevant to the photo (if the metadata is available). The initial grouping is date and time and then grouped further based on location.
If you go back through messages and save photos they will be saved in Moments when the picture was
taken, not when you received it and not when you saved it.
In Albums > All Photos will be in the order you saved it.
This is intentional design and its very important. An example of its intended use.....say you goto your families house for dinner and everyone is taking pictures, than you goto your friends house and everyone is taking pictures and finally you goto some sort of concert or sporting event where everyone its taking pictures. A week goes by and you ask for some of the photos that were taken and some trickle in through group messages and other various means and you save them.
All the photos should be listed as actual moments. So you'll have a group of photos from your families house. You'll have another group of photos from your friends house. And finally you'll have another group from the concert or sporting event that evening.
So to edit the initial date and time group you'll need to modify the date and time the photo was
taken (not the time it was created or modified which is a common mistake). To edit the location group (if applicable) you'll just need to modify the location. I'm sure there are plenty of ways but I just use the Photos app on the Mac.
To do this you'll need to open the photos app and highlight you pic you want to modify and right click "get info" or press the "I" button at the top right of the photos app. Than double click the date underneath the photos name (IMG_4530.JPG in this case) and you'll get a window like this.
Keep in mind we are arbitrarily adjusting the date and time the photo was
taken, not the time it was created (saved to your phone) or modified.
But from there you just adjust to the day you want this Moment to be.
Adjusting location is just as easy. You can select the city, state, country to make large changes and/or drag the thumbnail to make small adjustments.
I'm sure there is other software for Mac and PC, maybe even apps for the iPhone but I'm not sure I never looked for anything else.
If you are just trying to find photos faster I highly recommend the search function. You can type in general things (dogs, cars, trees, refrigerator, watch, wedding etc etc you'll need to experiment), dates, locations (streets, cities, countries), known people, etc etc. Once you get used too it its very helpful.
I don't recommend arbitrarily modifying moments since you'll scrub all the actually data off the photo to put incorrect info. Its odd if your life moments have snow in the summer and incorrect dates of sentimental pictures (pictures of relatives that have passed away or births or whatever and you are unable to remember exactly when the photo was taken). Its a free country though so do as you please but keep in mind the change is permanent. So if you resend the photo via a means that keeps the metadata the new owner of the photo will have your modified dates (falsified information! lol jk).