There's no colour palette rule per se, but because pixel art is about pixel-level control, that means you should also have control of your colours. Picking them carelessly is a bad idea. More importantly, picking colours carelessly leads to worse artwork, because the colours lack unity. Even non-pixel art artists often limit their palettes and reuse colours because of how it improves their work.

No it was drawn pixel by pixel with a 1 pt hard pencil tool in Photoshop. I didn't really pay attention to my colors though or try to limit it. I often just click color palette and click somewhere on the gradient I like.

Did not know there was a color palette rule, sorry.

You have quite a few colours in this image that are only used in 1-2 pixels. Did you use some "dirty" tools for this, like brushes and gradients?