It is really hard to determine the condition of your parrot's beak based on a written description. I don't think any of us here are avian vets, so if you're really concerned, you should check with your bird's doctor.
I have observed with my birds that the keratin sheath that makes up their beaks appear to have two layers, a bottom layer directly over the bone and a second, upper layer. This upper layer is sometimes chipped and worn back a good bit from the end of the beak. Take a look at the tip of the beak of the bird pictured on this page
http://www.birdchannel.com/bird-diet-and-health/bird-care/the-bird-beak.aspx (look under the line from the number 4 shown) and you'll see what I mean. The kind of chipping shown in this picture is just normal wear, and if your parrot has something similar, I'd say you have no cause for concern.
You shouldn't expect the wear to be exactly the same on both sides of the beak. Parrots didn't evolve in cages, and the metal bars and toys are hard on parrot beaks and can cause somewhat asymmetrical wear resulting from things like falls against bars or fighting with a bell.
If you can find an identifiable mark or scratch on your parrot's beak, watch it for several weeks and you will notice it slowly moving down the beak toward the tip as the keratin grows. (The keratin grows from the base, under the nostrils, toward the tip.)
Again, if you're really concerned, check with your vet.