Being underweight can cause many health problems, just like being overweight can. It can put unnecessary stress on your heart and other organs.
Also, being underweight does not mean you're anorexic or have an eating disorder - some people are naturally underweight. How are your eating habits? If you feel like you're restricting or scared of gaining weight, then you may have a problem. If so, check out the eating disorders board on this site.
Either way, you should talk to your parents about your concerns. Take your health seriously, go see a doctor to make sure everything is working as it should.
I do have to say that's very thin and an anorexic BMI, but it may depend upon your age as well. If you're in your early teens and after a growth spurt, it may be normal. However, if you're closer to 18 years old, it's quite underweight and may even be dangerous especially if you are obsessing over your weight, dieting, or overexercising. I had very severe anorexia when I was in college. I'm 5'4" and at my lowest weighed about 80 lb. All my periods stopped and I generally started to feel horrible (tired, dizzy, heart hurt) once my weight went below 105 lb. I was severely restricting my food intake and overexercising a lot. If you think you have an eating disorder, please do get help. It's nothing to mess around with and the longer you struggle with it, the harder and harder recovery becomes.
I totally agree with the last poster. It sounds like you might be (or probably are) underweight, you should really have a check up just to make sure there is nothing wrong. Any medical personnel that hears a patient say they have pain in their chest will immediately want to do some checking. Please talk to your parents immediately and ask them to have you checked. I don't want to put any ideas in your head, but I know enough from personal experience with a family member that anorexia can defiinitely affect your heart. So please talk to your parents. If they don't think there is any concern, just let them know that you will feel better by getting a check up and you will stop stressing about it.
For a teenage girl, such a low BMI is considered malnutrition by the CDC.
It would be expected to occur in 3% of 13 year old girls and in vanishingly small numbers in anyone older...and those are statistics for a FAT nation, the U.S.
(Median 17 year old girl has a BMI of 21 and only 3% have a BMI under 16.8.)