How can I grab my photos from iPhone that won't stay on?

I’ve used this site and products before to replace a battery. When I went to replace the shattered screen on my current iPhone 7 plus, I went with another (worse) site. They didn’t send me the right screwdrivers and when it came time to remove my front camera and switch it over I was completely unable and was beginning to strip screws. So I carefully put everything together and reconnected all of the appropriate cables and put the shattered screen back on the phone.

Now my 7 plus won’t stay on for more than 3 minutes of use at a time. Everything else is fine, everything loads up, but as soon as I open too many apps, stream a video on any kind of app, or just stay on it browsing for more than three minutes, the phone automatically reboots. If it’s not plugged in, it might turn on once, and then just shuts off. If it is plugged in, it shows battery percentage at 1%, 2%, or 100% but never anything in between, and it never stays on more than 3 minutes regardless of the percentage. Completely frustrated, I just bought a new phone.

Here’s where I need your help. I can use the three minute intervals to copy everything from notes, to copy my contacts etc. but I’d like to have the pictures. My last iTunes backup was a few months ago and I’ve never used the iCloud. No matter if the phone is plugged in, it only stays on long enough to start the back up and then shuts off and ends it halfway through. Even with the AT&T mobile transfer app it shut off after beginning, and trying to backup to iCloud via WiFi it shut off in the middle. What do I do?