Well u have a few options here, and more if u have money to support urself. One of the best ways to slowly start losing weight is change ur diet...obviously this costs money so if u dont have a job or make enough to buy ur own food (ill assume u live at home) then it will be more difficult, but if u DO, id def start with a diet change. avoid carbs and excess sugars, anything with lots of preservatives in it, fast food, etc.
another thing u can do, and this will help whether u eat healthy or not, is count calories. u can find sites online where u put ur height weight age sex and daily exercise and it will tell u how many calories to consume each day. from there u need to count EVERY calorie u put in ur body and make sure u dont go over what it says u should be eating. this may sound easy but its alot more work than ud think, however it will help
yet another tip is eat often but in smaller amounts. eating 5 small meals a day verses 1-2 large ones will help stabilize ur metabolism which keeps ur body from going into panic mode and storing so much fat.
DONT SKIP BREAKFAST...EVER
excercise: 1st things 1st, its HARRDDDD to get urself up and actually doing it, but every day u force urself out of the computer chair and into some form of exercise, it gets easier and easier. i can understand the selfconcious (gg bad spelling)
thing so id suggest jogging or even walking around ur neighborhood, and if even that bothers u try doing it later at night when less people are out and u can feel at ease
hope some of this helps, most are methods i used when i needed to shed some weight