Combat > Damage
If your attack succeeds, you deal damage. The type of weapon used determines the amount of damage you deal.
Damage reduces a target’s current hit points.
Note also Combat > Hit Points:
When your hit point total reaches 0, you're disabled. When it reaches –1, you're dying. When it gets to a negative amount equal to your Constitution score, you're dead. See Injury and Death, for more information.
These thresholds at 0, −1, and −Constitution make no senses if you tracked damage taken as a positive number; you instead track current HP, a value that you subtract any instance of damage taken from.
Finally, Combat > Nonlethal Damage > Dealing Nonlethal Damage
Dealing Nonlethal Damage
Certain attacks deal nonlethal damage. Other effects, such as heat or being exhausted, also deal nonlethal damage. When you take nonlethal damage, keep a running total of how much you've accumulated. Do not deduct the nonlethal damage number from your current hit points. It is not "real" damage. Instead, when your nonlethal damage equals your current hit points, you're staggered (see below), and when it exceeds your current hit points, you fall unconscious.
Here we see that you are running nonlethal damage correctly, but see how it is explicitly contrasted against “real” damage which does reduce current hit points. Again, the thresholds (equaling or exceeding current HP) only make sense if current HP is going down while nonlethal damage is going up (so they can meet and cross).