No, you are not overweight at all, and whoever told you it was a good idea to even consider a "diet" was very mistaken. Don't listen to them.
At 120 pounds and 5'5", your Body Mass Index is 20.0, which is about the middle of the normal range -- an excellent place to be.
Underweight = <18.5
Normal weight = 18.5–24.9
Overweight = 25–29.9
Obesity = BMI of 30 or greater
The fact that you're running 35 miles a week tells me you're in no danger of slipping into being overweight anytime soon. And of course you love carbs! Everyone loves carbs, but you can afford to enjoy them, so don't worry about it as long as you stay away from soft drinks and crap fast food.
In fact, as an athlete, you need carbs. Running 6 miles a day requires a significant amount of energy, and carbs are generally the best way of supplying that before and during your runs. Carbs before/during and protein after is usually the best approach. The carbs supply immediate energy for the run, and the protein after supplies the materials your body needs to build muscle.