Hi, 57kgs is a good weight for your age. Losing 20kgs will make you under 6 stone. This is not healthy. Tone up at home you don't need a gym. If you want exercises I'll help no cost, I teach and train fitness for all ages with minimal equipment. You just need someone to tell you what to do.
I feel you as I was really fat from 17-19yrs old and it's hard when almost everyone tease you for it. I did lose weight though, thanks to my part time job as a kitchen service crew in a restaurant. It seems I just need to be more active. Just be sure you lose healthily. I think it is easier if you aim to lose just 8lb in a month. It will be easier to maintain too. The heavier and taller you are, the easier it is to lose weight. And since you are just 16, you still have really good metabolism.