Calorie deficit would be the best way to go about in my opinion. This is possibly the best non-invasive treatment for weight loss, though it does require good commitment. Avoid saturated and trans fat food, as well as oily food. Ensure, with your calorie deficit, you are having your essential vitamins and minerals, proteins, carbs and the healthy fats (basically a balanced diet)
Nutrition definitely plays a part to your height, however, there’s a hormone called Growth Hormone that depends on your height, as well as other hormones such as oestrogen. I believe you might have already gotten your growth spurt by 14 or midway into it, but free fatty acids and high glucose levels can actually impact your growth hormone levels and decrease the secretion of the hormone. So this is why it’s important that your diet avoids high glucose and high fats as this can reduce the amount of growth hormone.
As long as you are having a balanced diet and you don’t severely starve yourself (1500 calories should be okay).
Now with your HIIT, I suggest maybe trying to do intermittent fasting, but do double check if you are okay doing this. Essentially, when the body is in the state of fasting, they typically will tend to use up more fat than carbohydrates. As you train your cardio, your body learns to use your fats first before your glucose, so I suggest taking a look into that.
Hope this helps! Always consult with your GP about any questions to do with your health.