Is it healthy to be 93 pounds when you're a 5'4 14 year old girl?

Possibly!: It is important to remember that health is not dependent on weight alone! your BMI (body mass index) is in the 6th percentile so you are on the thin side. I would not recommend losing any wt! Health is based on having a healthy diet, adequate sleep (7-9 hrs), regular exercise, and healthy friendships. Being too light or too heavy can be unhealthy, but less than 5th percentile is underweight.

Not really . . .: By conventional standards, you would be considered underweight. Being underweight during your teenage years can actually lead to some pretty significant medical problems, and long term complications. If you have a strong family history/tendency toward being very thin, maybe this would just be 'genetics'. This is certainly a conversation that you should be having with your doctor.