Hello,
Let me start by telling you, I am a 14 year old male, and slightly underweight with no discovered allergies other than seasonal. Once about every few months, I start to randomly have a bad stomach ache at night. After about half an hour to an hour, I will throw up once, and only once. Although nobody in my family would be sick, I still throw up. It will be random, and sudden. It has been bothering me lately, and I want to figure out why this is happening. I think it might be lactose intolerance, but I am not 100%.

Have your parents take you to the doctor. Explain this to him/her. There are hundreds of reasons for symptoms like this, but we don't know your medical history, nor can we do the necessary lab work.

Could be anything, 1000's of possible answers. Tracking, exactly what you do, where you go and what you wear and more, while this happens, is one way to start