You should go see another doctor. None of that sounds normal. I have chest pain and dizzy spells from time to time too, but at some point will go get an EKG to see if something's wrong.
As for your body weight, you're barely above being underweight. Your
BMI is about 18.6 if I did the calculations right (54kg being just under 120 pounds), and the borderline for being underweight is 18.5. So yes, you're not at a very healthy weight.
The not wanting to eat could be due to depression or feeling down. When my ex broke up with me last fall, I lost 10 pounds over the Christmas season because I was working 6 days a week, and being depressed to the point where I was barely eating.
You could talk to your doctor about starting a new diet, and not diet-lose-weight, but diet as in figuring out how to get you to eat more and eat healthy things. Or talk to a nutritionist. Either way, you need to get your weight up a bit.