Greek yogurt does have a lot of protein, and I eat it every day, but it does go right through you. Something like meat sits in your stomach a lot longer, thus keeping you fuller. That's not to say that you shouldn't eat Greek yogurt, but try to get some meat in for some of your meals, too.
I've read that there is a limit to how much protein the body can absorb at one time - I can't remember off-hand, but I think it was 30 or 40 grams, but I also recall that there wasn't really a consensus on this. I have to eat 100+ grams a day because I malabsorb protein (my prealbumin level tanks if I don't get that much), but I spread it out throughout the day.