Is 89 pounds a healthy weight for a 5' 4 girl?

According to the BMI (Body Mass Index) the following categories are:

* Underweight = <18.5 * Normal weight = 18.5-24.9 * Overweight = 25-29.9 * Obesity = BMI of 30 or greater The BMI of a 5'4" girl weighing 89 lbs. is 15.3

You are underweight.

Whether this is due to undernourishment or malnourishment you definitely should see a doctor. If you are interested in how BMI is calculated you can wiki search BMI.