Chalk me up as another person who isn't great at this type of games but made it through the Last of Us without too much trouble. I can think of a couple spots where there was forced combat, and one particular that I had to retry a bunch, but the game just isn't that hard.
One thing that comes to mind is, if you want to go the combat rather than stealth route (because you're having trouble with the stealth) are you using explosives and molotovs to their maximum potential? Using a bottle or brick to make a noise and then following it up with an explosive or molotov is one way to clear out a bunch of enemies at once and give yourself room to operate. Also, don't be afraid to engage combat, kill a few guys, and then disengage and heal up. The game is designed in such a way that you can often run into another room and hide and while the enemies will be on full alert they won't be able to track you perfectly. Then you can set up an ambush or at least pull a couple away from the pack so you're not fighting everyone at once.
The Last of Us combat is often about managing encounters and setting them up to your advantage. If you go in guns blazing and try to just shoot everyone like it's Gears of War or Uncharted then yes, it is an extremely hard game, but if you use stealth and strategic explosives to reduce enemy numbers, and hit and run in combat, it becomes manageable, and, in my opinion, even fun.
Nothing quite like getting four guys to clump up investigating a thrown bottle only to set them on fire with a molotov and only have to mop up a few of their buddies to turn a very tough encounter into a very manageable one.