My First Nuzlocke seems too easy: Am I doing it wrong?

So let me preface by saying I haven't played Pokemon since about 2005, watched some playthroughs recently and wanted to try it out. I've gotten through gym 5 (Gen 3) without losing a team member yet. Which I remember him being particularly tough, so my question(s) for a true Nuzlocke is:

Are you not supposed to overgrind before gym fights? Am I just visiting a Poke Center too often? Is it just beginners luck?

I'm having fun, but it kind of feels just like a normal game just missing out on catching some of my favorites from back in the day.

EDIT: thank you for all the responses and feedback. When I had looked up the nuzlocke rules only the 3 main ones were listed: deaths, one catch per route, and nickname all Pokémon.

I will most likely continue this run with the addendum of not going over the next gyms ace level and try a new one with some of the rules you guys listed below.

I really appreciate the support and education of the different versions of Nuzlockes there are.