You still need calories for energy and most veggies do not have many calories, which might be partly why you have no energy. What eating disorder did you have? Anorexia and bulimia can wreck the body - do not do that again because you will pay for it many times over with possible permanent long term damage to your body and/or brain. The human body constantly fights to maintain homeostasis - it wants to remain constant and stable not slammed with sugars or starved / purged.
Sugar is like a drug so get used to not having the extreme sugar highs (and crashing lows). After splurging on sugars for so long your pancreas and insulin levels have likely not adjusted yet - give it time to adjust as the body switches to getting energy from non-sugar sources like fat. White rice and white bread can spike your blood sugar and cause your pancreas to dump insulin into the blood stream. Search and understand Glycemic Index and Glycemic load of different foods. Search and understand insulin and pancreas function. Insulin is estrogenic and contibutes to fat accumulation. The body protects itself from sugar loads by dumping insulin into the bloodstream and also turning the sugar into body fat.
So, you want to switch from eating sugars to eating more fats. Do not look at fat as a bad thing to eat. When trying to lose body fat yes it sounds counter-intuitive. Your body is designed to get energy from fat which is why your body stores fat instead of storing sugar. Train your body to burn fat by eating healthy fats and exercising. Eating sugar trains the body to burn sugar for energy. Eating fat trains the body to burn fat for energy.
If your body does not get enough calories it will store food as fat because it thinks it is starving. Eat calorie dense and nutrient dense foods like soft boiled eggs (eat the yolks and the whites, especially the yolks) avacados, salmon etc. Peas are rather dense for veggies and are a good source of protein. Your coconut oil is great just don't eat the cheap processed coconut oil.
Also, exercise if you aren't. And don't drink milk - it's loaded with estrogenic hormones, and you should be weaned off milk at your age anyway, and you aren't a cow.