Is my weight (102lb, 5ft7) unhealthy?

When I was 5'6" and 103 lb, people were worried. You are definately too skinny, but it sounds like you don't have an eating disorder. If you're eating normally and not exercising excessively and still losing weight, it's REALLY important that you go to the doctor to find out what's wrong. It could be as simple as an overactive thyroid.