This question is often asked, and the answer is relatively simple, but does need some explanation. Please read this entire answer and it will make more sense to you.
In YOUR case, the mirror is the more true representation of how you look, .... but .... that is only because of the very poor quality and lack of skill used in the photographs of yourself that you, or others, are taking.
The great majority of young people, particularly it seems on this forum, try to take photos of themselves by holding the camera, or cell phone, out at arms length with the flash blaring off. This is the absolute WORSE way a photo can be taken. By necessity, the lens has to be at the wide angle portion of it's focal range, and when close to a subject, this will cause distortion. Any wide angle lens will do this, be it cheap or expensive. So that is one strike against you already, your face is going to be distorted. Second is the on camera flash. I'm sure you must have a flashlight somewhere in the house. Turn the lights off in the bathroom, stand in front of the mirror, and shine the flashlight directly onto your face. You will see it is by no means complimentary to you. It is a very harsh, small, direct light source. This is the same as the on camera flash, except that the flash is even WORSE! You will ALWAYS look bad in a photo when a flash is blasting off near your face.
People are NOT seeing you as you are seeing yourself in your bad photos. People are not looking at you with distortion of your face or under a fraction of a second of harsh, hard, unflattering light, which is what your photos depict. People see you in correct proportions and the light is natural, ambient light, the same as you are seeing when looking in the mirror, or anywhere else for that matter.
Now, a REAL professional photographer WILL make you look good. In fact, it would be a huge insult to a pro photographer if he / she could not make you look MUCH BETTER than you look in a mirror. A true photographer will use large, highly diffused light that falls naturally on you and this light will even have direction that will give shape and dimension to your face. He will use a moderate telephoto lens that creates NO distortion of the human face. He will understand color balance so your skin tone is natural looking in the photo.
The glut of digital cameras in the the hands of everyone today has given them the delusion that all it takes to be a "photographer" is to buy a "professional camera". Nothing could be further from the truth. GOOD photography is still a skill based craft that requires knowledge, technique, study, and knowing how to use light, composition, and equipment to CREATE a great photograph. A pro photographer does not just snap a photo and then wonder why it looks so bad. AMATEURS waste their money on expensive cameras thinking it will make them good photographers. It does not, never has, and never will.
So don't judge all photos of you by the results of your own efforts or those of your friends. Pro photographers and studios exist for a reason. When you are sick, you go to a qualified doctor. When a car needs repair, it is taken to a qualified mechanic. When you want REAL photography, you need to hire the services of a REAL photographer.
Here is an example of a proper photograph of a young lady. As you can see, it is vastly better than an amateur snapshot, and she certainly looks much better in this photo than in any bathroom mirror!
http://www.lightanon.com/-/lightanon/detail.asp?LID=&photoID=10396105&cat=92463
steve