Hi Sooisme and welcome!
If you have Story Progression turned on and Aging turned off, all Sims will continue through their lives, but they won't grow older. It's a little confusing to me, actually, because how can marriages and births happen without growing older? But that's my understanding of how it works.
As for your question about everyone else aging while your Sim stays the same, another way to accomplish is this is to feed Life Fruit and/or Ambrosia to your Sim. Life Fruit will add one day to your Sim's life for each piece of fruit eaten. Ambrosia will reset the aging bar back to the beginning of your Sim's current age category (Young Adult, Adult, Elder).