I've removed my Gallery default app with NoBloat. NoBloat is a great app and I've used it to remove all of the bloatware that came with my Note 3. Yesterday I was playing with my phone, then I thought "well, I use QuickPic, so let me remove the Gallery app too". Well, not a great idea (especially not backing it up before doing it). Now, I can't access my pics from the corner of the Camera app. Is there anyway that I can get it back without resetting my phone (it just won't happen)? I've tried looking for the app at the Samsung Apps store but they don't keep it over there
No, you won't be able to get it back without a backup unless you know someone with the same phone who can back it up & provide you with a copy.
You also won't be able to update your system OTA in the future either, as updates check to make sure that all the apps that should be there are present. If they're not, they won't install.
Freezing apps rather than deleting is generally a much better idea.