Do low carb-high protein diets really work?

It seems to me that eating basically only meat, yogurt, and cheese wont work, but I researched it online and it says that doctors recommend it the most to their over-weight patients. I'm going to be part of a Quinceanera of my best friend's party and Im kinda embarrased about my shape. Last night I jogged in place for 40 minutes (i counted it as 4 miles because it takes me about 10 minutes a mile)some arm excersises and killers(rosies). So far today I've eaten about half a cup of yogurt with granola, an iced tea(no sugar)and about 3 ounces of pan-fried chicken , skinless. Is this okay? It seems like it's not enough food, but I can't think of anything else that's low cal that's not meat or dairy. Can anyone help? Has this worked for anyone? I'm about 5'3.5, 5'4 and weigh MAYBE about 150 pounds, but could be less. Im not sure. I just want to lose 20 pounds, but how long will it take?