**These steps will work the same in either Illustrator or Photoshop**
Illustrator may be easier for what you need but if you want to use Photoshop you can still follow these steps:
Why don't you actually make a paper plane and take a photo of it from what ever angle you need e.g. from the top or from the side and then import the image into Photoshop.
Then create a new layer and use the pen tool to draw paths over the plane until it looks like the one you made and then fill in the path shapes to create your "plane".
All you have to do then is remove the layer with the photo of the plane on and you're left with the image you drew.
Just save that image with a transparent background and implement it into your game how you see fit.