AirPods should be able to remember more devices.
Unfortunately, Windows does not support automatic switching between devices, as Apple devices do.
Try this:
Open the Bluetooth settings on your Windows PC, and press and hold the button on your AirPods case until the LED lights up in white (Remember to leave your AirPods in the case) and pair your AirPods with Windows.
Okay, now your AirPods are paired with Windows and now you want to use them again on your iPhone. First, disconnect (not delete) your AirPods from Windows - I assume your AirPods are already paired with your iPhone. Take your AirPods in your ears and on your iPhone go to: Settings -> Bluetooth and connect to your AirPods manually.
Does it work?