Am I really fat? Does it even matter? I'm a female, age 14, I'm 5'2" and 131.8 lbs. I have a large frame and everywhere I've looked they say 128-140 lbs is an "ideal" weight, but I feel like I look terribly fat?

At the age of 14 PLUS being a female..... You can be a tooth pick and still see yourself as obese! Listen to your doctor. If they say you are healthy, then chances are you need to look at the mirror with different "goggles" on meaning you need to CHANGE the way you see yourself, not change yourself.

you are in the right weight range but on the higher end. But not bad at all.

What you need is a scale that shows weight, body fat%, and water weight.

Body fat% is more an indicator of whether you are overweight or not, than BMI.