iTunes stores the most recent backup of your iPhone in ~/Library/Application Support/MobileSync/Backup/[ID] iTunes does not keep any history of your iPhone backups. It is a copy of the current state of your photos and other data on the iPhone.
To recover an earlier version of your iPhone backup relies on however you backup your Mac.
Time Machine backups include the MobileSync folders. So you could retrieve an old iPhone backup from Time Machine, replacing the current backup in ~/Library/Application Support/MobileSync/Backup/[ID], and then restore your iPhone. This would, of course, replace all your current photos (and other data) with that from the old backup. Probably, not quite what you want.
I suggest using iBackupBot which is able to open any folder on your Mac containing iPhone backups. So find an old iPhone backup in Time Machine, retrieve the whole folder to your Desktop (or somewhere convenient) and open it with iBackupBot. Your photos will be in the Media/DCIM/100Apple/ folder. You can then extract these to your Mac.
If you don't want to use additional software (like iBackupBot) then you can find your photos in the ~/Library/Application Support/MobileSync/Backup/[ID] folder of an old backup. The files have cryptic names and no file type, but your photos are all there - just hard to find. Sorting by size might help you get to the right files.
If you use some other backup method for your Mac, then use that to find and retrieve the old backup folder.
If you don't backup your Mac, or don't backup the MobileSync folder, then I am sorry to say you have lost them.
In future, I suggest you transfer all photos from the iPhone to your Mac using, for example, iCloud and Photo Stream.
Additional: No backup of Mac hard disk. Not all is lost - perhaps. In January your pictures were on your hard disk. Though they have since been deleted (by a more recent iTunes backup) at least some of the data which was you photo files is probably still there in the free space. This now getting well beyond the original question. Now we are talking about:
How to recover files which have been deleted from the hard disk. There are utilities which can help - for example Disk Drill. But, I think that should be new topic and that may get answers from those with recent experience of file recovery.
Factory Reset
I ended up doing a Factory Reset to clear off the "Other" data.
The key is that since the Other seemed to be backup related, I did not restore the phone from the backup. Instead, I selected "As a new phone".
One by one, I added back her apps, music and photos, watching the Other bar like a hawk.
The Other data remains virtually gone now only taking up 430Mb.
Best Answer
Is this device older than 2 years and has never been reset?
I can't tell you exactly what to do but this article quotes some possible solutions:
Do you happen to send and receive a lot of messages with multimedia? that could be clogging up some of your storage especially if you set the settings to delete messages to never.
How much space do you seen take by the
Othercategory?Othermay include:Check voicemails?
Try to reset Safari Cache and data.
EDIT: OP indicated that the issue is indeed with the "Other" category, this article has some tips on how to try and locate and free up space taken by various elements that make up this category.Also check this Apple forums thread. Download any mentioned software there after doing your own DD.
Here's what "Other" includes, in full: