The first thing I'd recommend for someone gaining weight as quickly as you are is to check with your doctor and have some simple blood tests done to make sure you don't have an underlying health issue such as hypothyroidism. Your thyroid controls your metabolism and if it's not functioning properly, you'll gain weight much more quickly than you would otherwise.
I agree that you should exercise to build muscle, but it's not true/misleading to say that muscle weighs more than fat. A pound is a pound, whether it consists of muscle or fat (or even fluid, for that matter). It's just that the molecules of muscle are packed so much more densely than the molecules of fat that more of them fit into a smaller space... compare muscle and fat to a rock and feathers - you can have a relatively small rock that weighs a pound, but look how much space it takes to hold a pound of feathers. That's because the rock is densely packed, like muscles and the feathers are fluffy, like fat...
It is not necessarily the weight you need to be concerned about. Next time you are at the gym ask for a body fat analysis. This number is much more important. Also drinking water throughout the day will help suppress your appetite. You may feel bloated and heavy but again this will help you lose the body fat, your weight is just a number keep in mind that muscle weighs more than fat and the more muscle you have on your body the more calories you will burn at rest. Build the muscle and the body fat will drop off. For post workout i would recommend a whey protein isolate, this will keep the calories down but provide your body with the immediate absorption your body will need to recover.