Boiled potatoes and eggs will not be toxic, and there will be no conflict between the two cooking at the same time. If you feel uncomfortable after eating, it is mostly because potatoes germinate or turn green and are not cooked.
If it is fully cooked, it will not be toxic, because there is a toxic substance called solanine in potatoes, which can agglutinate red blood cells in human blood. If the human body ingests a large amount of this substance, it will cause acute poisoning. This toxic substance is mostly concentrated in the potato skin, and the light will turn the potato skin blue. Solanine will increase with the deepening of the potato skin color, so it is necessary to peel it when eating, especially to clean the potato skin that has turned green.