Firstly, no, you are not anorexic, because anorexia is a mental health problem whereby people think they're too fat even though they're already skinny. If you don't think your size is a problem, then you're not anorexic.
But, I'm going to be honest with you here, you are eating ridiculously low amounts of food a day. If you do feel faint and dizzy there's a high probability that you're just malnourished- your body is lacking all the nutrients it needs for you to be healthy, and if you're stressed about UCAS on top of everything then that's obviously going to make you feel even worse.
You really really shouldn't skip lunch, your body needs this energy to keep you up during the afternoon. I would highly recommend starting just by eating lunch, because having 2 small meals a day is unhealthy no matter how small/thin you naturally are. If seeing a dietician helps you keep to a healthy food schedule, do it, but explain to them that you eat in small portions.
(Take this from someone who is 20 years old, 5'4 and weighs 99 pounds. My mum worries about my weight too but she knows that I eat 3 good meals a day as well as snacks, and that I excercise too.)