Add the rice, water, salt and cinnamon sticks to the bowl of a 6-quart or larger Instant Pot. Give it a stir and then lock the lid, making sure the valve is set to seal. Pressure cook on high for 5 minutes, and do a natural release for 10 minutes before manually releasing any residual steam inside.
Carefully open the Instant Pot and discard the cinnamon sticks. In a large bowl, whisk together the milk sugar, egg, vanilla, ground cinnamon and nutmeg. Stir into the cooked rice and set the machine to sauté on low.
Cook, stirring often, until the pudding has thickened, about 5 minutes. Turn off the machine and carefully remove the inner bowl. Stir in the butter and raisins and serve either warm or transfer to a container to chill until ready to serve. If the pudding thickens too much, you can thin it out with a splash or two of milk before eating.