First time trying, need help

Hello! I don't really know how to start this, so I'll go straight to the point: I'm sick of the way I look. These past days I've been feeling like crying just from looking at myself in the mirror, and instead of getting sad like usual I want to try and change, see if I can feel comfortable in my own skin.

Forgive me if any information is lacking, it's my first time posting here and I don't know much about weight loss, so if there's any mistakes please tell me.

I'm a 17 year old female, 155cm tall (around 5'1 I think?) and I currently weigh about 65 kg (143lb??). I've honestly been having a bad streak lately and thought about just not eating, but I know how dangerous that is and don't want to develop an eating disorder. I've talked with some friends that are also on diets and exercising and they recommended some apps to calculate the calories I need to eat everyday. According to MyFitnessPal I should be eating 1600. I don't know if that's okay, my friend tried to explain to me how that works but I didn't really understand. And the thing is, I don't move much and I'm a vegetarian (no meat, no fish and no eggs, but I do drink milk), so I don't know if I should buy some protein supplement or something. I also want to start exercising, the past two days I've been trying a routine to work on my belly but I'm a bit sick so I can't do much, although I want to start walking too when I get better.

Could you give me diet recommendations and exercise routines? Any other kind of advice is appreciated too. I really want to lose weight preferably before may, at least 10kg, but my ideal weight would be 49kg. I know that I will probably need more time and I'm fine with that, I just really want to change because I seriously can't stand my looks.

Also, I've tried losing weight before but I always gave up. Besides, I've never tried diets, and now that I've talked with my mother about wanting to lose weight I hope that I'll be able to follow one + exercise regularly.

Thank you in advance!