It's also possible that you just aren't finding all of the ammo that there is to find. While I know not to kill everything in the game, I usually kill most everything in the Prison area, and I come close to running out of ammo but I never run out. Consult gamefaqs.com, it might help (I personally like the guide by Minesweeper).

You may want to reexamine how you are killing the zombies. You can usually shoot a zombie three-ish times and it will go down. If you aren't being chased by more zombies, take out your knife and slash at it while it's down, you'll save ammo and you might even kill it while it's still down, though don't stand by its head. If you ever find that you have plenty of healing items, you can also shoot a zombie and make it fall, and then stand by its head. It will grab and bite Claire's leg, but then Claire will smash its head and it will "die." Also, the MP-100 is your friend. Don't waste it, but don't be afraid to use it.

If you need to dodge zombies, use the following technique which I find rather effective. Lure a zombie to you. When it gets close it will lunge forward a little and try to grab you. If you back up and stay far enough away while the zombie is trying to grab you it will eventually (after four or five steps) put its arms down and give up for a second (except for the ones with the glowing eyes and the doctor). This is your chance, run by it. Also, if you are being attacked by several zombies with no escape in site, lure them to you and let one bite you. While its biting you, the others will get closer, and when Claire pushes the zombie off of her all the nearby zombies will also be pushed back/down, thus your cue to run.