How to get my photos back onto my Iphone?

I had to get a new Iphone from Apple because my Wi-Fi was greyed out and not working. When she gave me the new phone she said I shouldn't restore my Iphone because I had problems with the software that would be transferred when I restored it. I couldn't back up my Iphone with Icloud but I could back it up on my computer. I have all my important photos on my Iphone so I'm just wondering when I did back it up to my computer where did all those pictures go so maybe I can put them on my Iphone a different way?

Just sync it from iCloud, but photos only. Go to the settings and then sync only the photos to your new iPhone.

I supports iPhone Manager from 4easysoft.com, it is really powerful.

If you have back up your photos, you can restore from the backup.

To restore information from a backup, use one of the following methods after connecting your iOS device to the computer with which you normally sync:
1. Right-click (or Control-click) the device and choose Restore from Backup
2. If you have a new phone, you can connect to iTunes and it will prompt to restore from your backup
Solution from Apple.com: http://support.apple.com/.../kb/ht1766

If you have no backup for your data on iPhone, iPhone data recovery software is your last shot! I used Tenorshare iTunes Data Recovery and it worked well. It's easy to use. Just a few clicks you can get all your data back. Here is a tutorial I found: https://www.any-data-recovery.com/topics/mobile-devices/iphone-photo-recovery.html

I think you can use a professional data recovery software to do the photos recovery for your iphone.
Try this one.