Q: Sync won't work, dont know if photos are stored on iTunes

At first I was syncing on my computer with my iPhone 6 and everything was working well. Then about a year ago I got a new laptop, and started syncing on there. I synced the phone once on the new machine and it went fine. But when I went to sync my phone on the new machine again, I got an error message saying that the iPhone could only be synced on machine and iTunes prompted me to erase the contents of my phone and replace them with the contents of my machine. Naturally, I didn't want my phone content deleted, so I didn't do it.

My old computer has all the traces of my IPhone off iTunes on there, but I do not have that computer anymore.

This has been going on for about a year now and I still haven't been able to get my iPhone to sync correctly. I'm planning on getting a new iPhone later this year so now I'm worried that the contents on my new phone wont carry over to the new phone.

Now, my apps, music etc.. I'm not worried about. I can replace that manually. My pictures are what worries me. With my troubles with iTunes, I don't know if my pictures are synced on my new machine, (The "sync pictures" option is turned off, and when I try and turn it on, I get the same error message). I did copy my pictures over to my computer's hard drive, but I don't know if that will sync back to my iPhone. So I don't know whether my pictures will transfer over to my new iPhone via iTunes. Here is a screenshot of the errors I was getting.