Welcome to our community.
I have to agree with the other 2 posters. For your height, you are actually underweight. I copied a portion of a height/weight chart for you to see what you should actually weigh. I don't know about your frame size (whether you are large boned or more petite).
Height Small Frame Medium Frame Large Frame
5'8" 126-139 136-150 146-167
Yallolorry is right; sometimes we don't see ourselves as we really are. Most of my teenage years, I spent feeling like I was fat, also. I'm short (only 5' tall) and up until I was in my 30', most of the time, I only weighed between 90-105, sometimes less, but I always felt fat and constantly felt like I needed to lose weight.
I also agree with yallolorry in that if you don't take good care of yourself (making sure you get the proper nutrients, etc), you could very well have health issues as you get older. If there are areas of your body that you don't like, maybe you just need to add an exercise routine to help firm up your muscles. Exercise can also make us feel a lot better about ourselves.
It's good that you eat fruit, but you also need to eat plenty of vegetables and foods that contain lean protein, such as meats, beans, nuts, low/no fat dairy, etc. Protein is what you need to build muscles and your bones need a lot of calcium to stay strong, plus all the other vitamins/minerals you need to be healthy.
I'd also suggest that you talk with someone in regards to your feelings about your body (parent, doctor or anyone else you trust) to help you see yourself more favorably. Losing 20 lbs would not be good for you and could possibly cause you to be malnourished.
We are all here for you.
Hi Helena - I hate to say this ans suspect you won't like it but please hear me out - I am an inch shorter than you and when I was 133 lbs everyone I know told me I was super slim - and I was! I've seen pictures of myself when I was younger and weighed 120lbs and I look way too thin, lots of people told me I was at the time and I didn't believe them but now I can see the evidence in the photos. I didn't actually look very well.
At 120 lbs you are actually underweight. If you think you are really fat then you are not seeing things as they are. You can check your body mass index here: http://www.nhlbisupport.com/bmi/
It's fairly normal for human beings not to recognise reality, we all dupe ourselves about one thing or another all the time! It's one of the interesting angles to getting older, trying to deal powerfully with reality and not just believe what our minds tell us about stuff. We are all to a greater or lesser degree bound up with stuff in our heads that isn't real.
However, telliing yourself you are fat when you're actually underweight can actually be dangerous. A lot of unpleasant stuff can go wrong with your body over time as a result of gettiing too skinny. I have a lot of friends who used to have eating disorders (not that I'm saying you do, obviously I can't know that!) who kept themselves too slim in their teens and twenties and now they are older are having real problems with their insides, bones and teeth.
tyharper is much shorter so her weight should be less than ours. the maths are pretty simple, if you put her weight and height into the bmi calculator you can see the difference.
I'd really suggest you talk to someone, perhaps a parent or even your doctor, about how you feel about your body and see if they can help you get some perspective on this.
If you'd find it helpful to start off with I'm always happy to listen and promise not to judge you - if you want to message me anytime please feel free.
peace and light
I think you're at a healthy weight. I'm 5 foot tall and 120 is considered healthy for me. So given your height, you should be fine. I don't mean to sound mean if that's what you hear. Just keep up the good work.