I've done same. I LUV bananas!!!
But if its not a banana, its another type of fruit or some low-fat yogurt. I'm not a nutritionist or scientist by any means, but I think the natural sugars found in fruit can satisfy your urge when you want to eat something sweet.
In addition to the fruit or yougurt, considering I'm a choco-holic, I've found eating a mini tootsie roll or a miniture piece of mint-flavored chocolate can do the trick too. I'm not sure, but I think due to the constant chewing on the tootsie roll, you feel like you've put in enough work just to get something sweet in your mouth, you don't need any more. Where as the mint-chocolate satisfies your sweet's need with, well, chocolate and then makes you feel refreshed at the same time with the minty flavor. Kind of like brushing your teeth after eating chocolate, you don't want anything but maybe some milk or water. (At least that's how I feel after a piece, it totally washes away my craving of more sweets). I also like to drink a small glass of choclate milk, which has the same effect.
As for eating 2-3 banans a day, you don't want to do that unless they're small bananas. Your body can only handle so much potassium, and if you ovedue it, you could have some side affects such as weakening in your muscles or abnormal heart rhythms. Bananas are a great source of potassium, but your also eating other potassium rich foods, such as other fruits, some vegetables and fish.
And in reguards to the fat content, don't worry about it. Bananas don't produce any fat, cholesterol, or sodium. They're actually a good source for potassium, vitamin B6, vitamin C, and fiber. If you are watching your calories, eat baby bananas. They're about 50-60 calories each. But honestly, the most calorific banana would be less than 150. So your still good.
Best of Luck!