My bmi is about 15 (175cm and 46kg), thinness seems to 'run in the family', but should I be worried about my weight?

Yes, it can still be familial, but your BMI is really low, you want to be evaluated for reasons to be thin, you didn't mention your age, and I am not sure if you have other symptoms, as whether you feel weak, your menses, other bodily functions, habitus etc.. You may want to start with your primary doctor who would refer you to an Endocrinologist, good luck.