My Car makes loud fan sound at start up

Past couple weeks, I've noticed my car has been making a very loud revving sound or over heating sound at start up. It basically sounds like a loud fan starting up. Last week when I was driving my engine over heat symbol came on in yellow then seconds later turned to red, then seconds later my car came to a stop. I let it cool down and parked to take a look under the hood. I noticed there was no Anti freeze in my car. I filled it up and then thought the noise would go away as I thought maybe the sound was from depleted liquid in the compartment. Any clue is to what this sound is from or being caused by?