Is a bmi of 17.5 (5'7.75, 114lb) at 14 bad? never gone above 119lb (3 years ago). how bad is it to be underweight? is this badly underweight? taking medications that frequently cause weight gain (sertraline currently, 150mg)?

A BMI of 17.5 at 14y is considered within the healthy range for young women. 20 is considered the average BMI at that age, but factors such as muscle mass & bone structure give us the "healthy range" we consider. I suspect you will put on more muscle mass as you finish your transition to womanhood. Discuss any concerns with your doc, but your numbers seem fine to me.