why did my chick die
Sounds like Coccidiosis. You will need to treat with Corid which can be found at your local feed store.
Dosage for Cocci is 1 1/2 teaspoons Corid powder per gallon or 2 teaspoons of 9.6% Corid liquid per gallon
Give for 5-7 days - make sure this is the ONLY water available during that time period. Mix a fresh batch at least once a day.
Give some probiotics or plain yogurt, and some poultry vitamins when they finish the Corid.
Poor thing she is lonely. You can try giving her a stuffed animal to snuggle with and put a mirror in the brooder so she can see herself until you decide if you can find her a buddy or two.