Is this a healthy weight I'm 16 years old 5 ft 3 and 105 pounds?

Yes, as your BMI (Body Mass Index) is 18.2. Between 18.5 and 24.9 is cosidered to be "normal" or "healthy" weight. However, this doesn't take into account muscle mass, body type, ect. Also, only a few tenths of a point off isn't much, so 106 lbs. is on the thinner side of average weight.