Why does my cast iron skillet keep rusting even though I dry it thoroughly?

I recently inherited a cast iron skillet from my grandma and have been really excited to start using it. I season it carefully and make sure to dry it completely after every wash - sometimes even heating it on the stove to evaporate any moisture. However, despite all that, I keep noticing small rust spots forming within a week or two. I live in a pretty humid apartment, but I store the skillet inside a cabinet with a silica gel packet. I've read that wiping it with a thin layer of oil after drying helps, and I do that too. What am I missing here? Could humidity alone cause this much rust? Should I be seasoning it more often or changing my cleaning routine? Any tips for keeping it rust-free in a humid environment?