Headset not found on Xperia L
After removing the pairing from the phone, the phone won't be able to see the headset in its normal mode any more. To connect to it again, you need to pair the phone with the headset again. To make the headset visible again, you need to put it into a special "pairing mode" which makes it visible to all devices for a short time.

The way of doing this varies from one headset to another, but typically you might hold down the power button for a longer time, until the light on the headset blinks (if there is one). On headsets with a volume control, you might need to hold one of the volume buttons before pressing the power button. (I've seen that on a Jabra headset.) With the headset in its pairing mode, search for devices from your phone and you should be able to see it and pair with it. After that, the phone will be able to connect to it automatically, like before you deleted the pairing.

It's very unusual for peripherals to only be able to hold one pairing at a time, so once your headset is paired with both the PC and the phone, you should be able to connect to either. You can only connect to one at a time, though. To learn more about how Bluetooth pairing works and pairing with multiple devices, you might like to read my related answer.