Making a chirping-gurgling noise?

Where is the noise coming from, the engine bay? inside the car? Can you please shoot a quick video with your phone so I can hear the noise? That way I can tell for sure what's going on. You can upload it here with your response. We need to hear the noise, so we know which direction to go to help you fix the car. It takes time to upload so please be patient.

This guide may help:

https://www.2carpros.com/articles/engine-noises

To me it sounds like the serpentine belt, or the heater core has an air bubble in it. I would wait until the engine is cold and then open the radiator cap to check the coolant level. Also, if the replacement belt is of a low quality, I would swap it out for a new one. While the engine is running inspect the belt operating, if there is a lot of vibration the tensioner can be bad as well. Check out the images (below). Please upload pictures or videos in your response to the problem so we can see what's going on.

Thanks for the video. It does sound like there is air in the heater core. I would wait until the engine is cold and then check the coolant level in the radiator. Can you please move the HVAC controls from hot to cold and then from floor to defrost to see if the noise changes?