Sweetie, I suggest you to have your eyes checked by an eye doctor immediately. Dark brown spots on the whites of the eyes can be a sign of some kind of eye problems. But they can be just the yellow tints if you are a heavy smoker. If they were the later, you may need to give up smoking or smoke less in future so that the smokes will not tint your whites of your eyes anymore. If they are moles, often they will not do great damage to your eyes. But if they are some kind of tumour, they can be very dangerous. The tumour will show a sign of growing up. And you may need to turn to medical treatment immediately. But I hope it won't be the last situation. Good luck!
Before give you some suggestions to get rid of the dark brown spots, I need to know what causes this. If it is the macular degeneration (a kind of eye disease) which often happens to senior citizens, you may need to turn to doctors immediately. It is said that there some kinds of pills that contain many kinds of vitamins and nutrients that can prevent the development of macular degeneration. But some people doubt that whether it works or not. But I suggest you to take good care of your eyes in your daily life. You can provide your eyes with various kinds of vitamins and nutrients in your diets. This can be a good way to prevent macular degeneration from happening. Besides, you may need to protect your eyes in some environments. You can wear a pair of sunglasses to protect your eyes. Too much exposure to sunlight will lead to macular degeneration. A pair of sunglasses will block the harmful UV rays and protect your eyes. Hope this helped!