Whenever I play Call of Duty, or dust 514, Internet is completely fine. This only happens when I play TLOU
Have you tested your latency (ping tests) to check how stable they are? I had a "good" connection with a ridiculously unstable ping which was why I was freezing. I switched my ISP and haven't had the issue since.
If that were the problem would it not cause problems with other online games?
Depends. I mean, different games allow higher degrees of packet loss than others, TLoU uses a much stricter netcode to stop people from lag killing when their latency spikes. If you're using wireless, try hooking your ps3 up to your router/modem to get a more stable connection and see if that helps.