It's certainly not a game to everyone's tastes given its snail's pace and the fact that you can log in to find someone's gnawed on your brains during the night when you couldn't do anything about it, but you could make things a lot easier on yourself than they are at the moment.
It's really hard to break through barricades when you're at a low level, and once you've got enough XP to buy free running you'll almost never need to unless someone over-barricades a building you want kept at VSB. With 30 AP you would have been much better served just wandering around looking for a VSB building instead.
Cop's also a tricky starting class, since without free running it's hard to get the ammo for the pistol which is your best way of getting XP. If you're in a fire station anyway look for an axe, you'll miss a lot attacking with one (base accuracy is a poor 10%) but it ought to help you nonetheless, and flare guns will be useful to you too. Their accuracy is poor, but they do give an impressive 15 HP damage (30 if you attack the target with a fuel can first) and since you already have basic firearms training their accuracy is maxed out for you already. Also, you'll end up killing more zombies faster if you take the time to stock up on a lot of supplies before venturing out. Even if every shot hit, one loaded pistol will only do 30 HP of damage so not enough to drop a healthy zombie. That might sound a bit disheartening, but killing just two fully healthy zombies will give you more than enough XP for any skill so it's not actually too bad.
Though you spend pretty much all of your time running for your life when you start once you've got a decent skill set you can do a lot more, as well as dropping zombies a lot easier (100 XP will buy you the skill to bump your current pistol accuracy to 55%, which ought to ease your frustrations). A good location will make your life easier too. If you're near Pegton I'd recommend going north to Pitneybank and operating out of the fort. The barricades are typically kept at VSB, there's the ammo you need and you should be able to find enough zombies to kill to the south and west.