I'm 16 and want to loose weight but need help...?

I know I can loose weight because I’ve lost a stone in just over a month before, but because with everything that goes on in my life at home at the moment and the stress at school, I’ve been on abit of an emotional rollercoaster and haven’t been in the right mind set to loose weight. I’m 5ft 3” and weigh around 13stone (wayyy too heavy, I know). As I’ve just finished my GCSE’s I’ve got 8 weeks of no school and enough time to loose weight (I hope) before I go to college. I know my problem isn’t fizzy drinks, sweets and junk food because I hardly ever eat that; I think it’s just my laziness (spending too much time with video games), too much snaking and not enough healthy foods. The last two weeks I’ve been changing my diet by eating more fruit and snacking on healthy things like humus and celery, sunflower seeds etc. , but I know I need to be doing more exercise and that’s one thing that I don’t know if I can do. I started doing sit-ups this morning and did 45mins on an exercise bike that has been lying around the house collecting dust. I would go to the gym because I really liked doing the boxercise when I was doing P.E last year, but I get anxious, paranoid and shy when I’m walking around strangers or talking to them so I doubt I’d cope well in a Gym. Sometimes I think to myself that I’m never gonna loose any weight and I should give up, but I know that’ll just put me in a worse situation. I really don’t know how to go about this, but I’ve got 8 weeks before I start college and I have to try and stay positive and try and stick to this. I don’t know how loose weight the right way and need someone’s help, please…?