My face looks weird when I take a picture with the front facing camera.?

When you look in the mirror, you are seeing a backwards version of your face, and that is what you are used to seeing, but your phone camera is not reversed so it looks weird.
I have attached a photo of Abraham Lincoln, and next to it is what he saw whenever he looked at himself in the mirror. As you can see, the mirror image looks weird, because it's not what you are used to seeing. And the photo probably looked weird to him. This is probably why your face looks weird on the camera.

With your front camera you are experiencing "Fish Eye" effect. Try to keep the camera away from your face as far as you can, this will minimize the fish eye effect. This problem is due to your front camera.

That's because your phone has a wide angle lens that causes wide angle distortion when you hold it at arms length, too close to your face.

Congratulations!! You just found out why phones are no good for taking selfies.

http://keerok.wordpress.com/2014/12/17/which-is-more-accurate-the-camera-or-the-mirror-or-the-most-inconsequential-adolescent-question-of-all-time/

A phone's front facing camera is very poor optically and at an arm's length, uses wide angle to get your head into the shot. At wide angle, distortion is pronounced making you look more than just slightly different from how you really look like. Knowledgeable photographers avoid all of these when taking portraits so they can make anyone look as good if not better than they really are.