I'd be fine for the whole day, but then when I eat my meal, half way through I'd start to feel really sick and wouldn't be able to eat anymore, even if I'm really hungry. I'm only 15, and would like to know what's wrong?

We can't possibly diagnose this, so you are going to have to talk to a parent about seeing a doctor. You could have anything from constipation to a food allergy to an ulcer, gall stones, or appendicitis (although you are young for some of those).
If you are female you could be pre menstrual and if sexually active, pregnant.
As you can see we don't know enough about you and a visit in person to your doctor is needed.

It concerns me that you go all day without eating until dinner time? That's not good for your health at all. I can't tell if that's what you are saying or not.
There's an old saying: eat like a king in the morning, a prince at noon, and a pauper at night.

You're your MEAL, do you mean Dinner, are you eating Breakfeast and Lunch ? If so, are you feeling sick then also ?

If you are not eating them, there is most likely about 1/2 the issue.

Also what are you eating,