Hey!
If you are trying to lose weight, then you are very likely going to have to restrict your food intake. In my own experience, exercise alone will not lead to weight loss. I think that's because exercise can make people hungrier, or if not, it makes them think it's "OK" to eat more since they did all that exercise.
In reality, exercise does not burn very many calories--but it improves the ability of the body to burn fat for energy. That and wanting to be healthier are why exercise is good.
So look into ways to restrict your food. Some people use a formal program like Sugar Busters, South Beach, You on a Diet, Atkins, Weight Watchers, etc. Others follow plans like calorie counting. But what all these plans have in common is that you eat less than you burn, and that's how you lose weight.
Also, at 5'6" and 151, you can expect to lose weight pretty slowly--more slowly than someone at, say, 181. So, you need to keep that in mind so you don't get discouraged.
As for the scale--that kind of difference is within the range of error of the scale and water weight fluctuation, so I wouldn't pay any attention to it. Basically you weigh the same.
Good luck!
Jay