Ugh! I'm so sorry. This is terrible!
Yes, please turn on iCloud backup or use Dropbox or Google Photo or some form of offsite backup. Even with a successful iTunes backup, you're only one fire/flood/theft away from losing local copies anyway.
There might be data recovery services you can try, though they could be expensive. If you ever mailed/messaged photos, those could be in your sent folders or the people you sent them to could have copies.
Also, if you backed up the computer with iTunes, there could be an older backup of your iPhone for you to try.