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Here is a calculator of ideal weight. According to this the medical recommendation is 88 - 116 pounds for your height which you are right smack in the middle. It also explains that often people think their ideal weight should be significantly less (in your case 97 pounds).

BMI (Body Mass Index) is another method used for answering questions like yours. If we use a weight in the middle of those you gave (102) we get a total of 22.1. The scale is broken down as follows:

Underweight = <18.5
Normal weight = 18.5-24.9
Overweight = 25-29.9
Obesity = BMI of 30 or greater

As you can see, you fall into the Normal Weight category.
The site I used for this can be found here.