Do you think it's right to reset the counter if you only search for porn?

Not a reset.Its like you want to quit eating cookies and decide to remove the lid from the cookie jar and resisted grabbing a cookie.

 

As my main goal is to refrain from intentionally seeking out pornography, I would view it as a relapse.

However, it's not like this is some sort of competition for which we must all follow the same rules. If you view it as a relapse, reset the counter. If not, keep going.

 

In that case, I'd view it as a relapse. As @2525 said above, you might be able to look at P once or twice without giving in, but that won't last. If you start searching it out, you will fall back into cycles of heavy use.

Either way though, don't worry about it too much. Think about what caused you to intentionally search it out and create an action plan for the next time the urge strikes (do 50 pushups, 50 situps, 50 mountain climbers, for example, or watch a nofap success video and write down 3 key takeaways from it that you will apply to your own life).