I backed up my iPhone and then did a sync and the iPhone is missing photos and so is my Mac and my phone will not let me delete them or on my iMac either.

So I bought a used Mac from my friend. I have the udated software and an iPhone 5 with the newest software. I have backed up my phone at least 4 times and all the photos and videos I need and wanted were on the phone. I did a backup and synce last night to itunes and now my phone has random old photos on it and I can't remove them or delete them. I also tried to restart iphoto and uninstall it and now it asking me to buy it for my Mac. I looked in the library for the photos and they are not there and used the preview option for it. Don't know how to recover or find them on my Mac. I have to have these photos for a company meeting and can't reproduce. Since the new updates with Mac and iPhone with the OS7 it has been really wierd and NOT working right. Also something to point out is that the events on my phone show up for the folders but they don't show up on my mac and didn't before. They only show up as dates but on my phone show as names that gave them. Help please! My presention is on the line. I've not been happy when I made the switch to everything apple. 😟