If Muscle Weighs More Than Fat, I'm Going To Weigh MORE If I Start Exercising???

I'm 5'8 1/2" and naturally lean, but it's all blubber. I'm one of those skinny-fat girls. Look thin in clothes, but chubby in a bikini. So I decided to start exercising because I want to weigh 120, ten pounds less than my current, but then I find out that muscle weighs 4 times as much as fat. So if I tone up, does that mean the scale #s will blow up?