My bluetooth headphone is paired however sound is still from my phone?

Can Bluetooth device connect to several devices at once? Is that where
the confusion is?

Yes, but you can play sound from only one of the connected devices at a point in time, not both.

For example, my SBH80 headphone from Sony supports connecting two or three devices to it. But there's a catch. You could only listen to sound coming from the device that connected to the headphone first. In other cases, none will play through the headphone. Some headphones are kinda designed to play sound in a first-come-first-serve approach. Others get confused, and don't play anything at all.

To get your music playing, ensure only one device is connected to the headset.

Usually I turned on my headphone and I will be listening to my
smartphone sound right away. Now it isn't.

This is happening because your computer probably connected to headphone first. Disconnect PC and sound should resume automatically. If it doesn't automatically, re-pair (not take to the repair shop!) the headphone with the phone.