This kind of hyperpigmentation is quite a common problem, and can be due to several reasons. The darkening of your neck skin is probably just a simple tan - for most people, the neck and hands are areas that are almost always exposed. As a result, they receive a lot more sunlight than the rest of the body, and as you know, sunlight causes the skin to tan. As a result, the neck and hands of most people tend to be darker than the rest of the body. This is nothing to worry about; it is completely harmless, and the only problem is that the contrast with the rest of the skin tends to look a bit odd. The best way to get rid of this tan, just like any other, is to avoid exposure to sunlight from now on. It is not really practical to always wear gloves and a scarf outdoors, but you can certainly wear clothes that have higher collars. This will protect your neck to a great extent. A hat will also provide some shade, thus minimizing exposure of your neck skin to sunlight. In addition, regularly applying sunscreen whenever you go outdoors during the day will provide another layer of protection. And of course, whenever possible, you should simply avoid being outdoors during the day, especially in the afternoon when the sunlight is particularly harsh.
The dark areas of skin around your mouth are slightly different. They too are the result of increased melanin production in response to exposure to sunlight, but this is only partly responsible for their formation. The condition is known as melasma or chloasma, and is thought to be related to hormone levels in the body. With a simple tan, all exposed skin darkens evenly, but with chloasma, patches of exposed skin darken more than the surrounding areas, even though the exposure may be the same. This is sometimes genetic, but in other cases may be related to some underlying health problem such as a thyroid condition. It is also thought to be related to hormone replacement pills and oral contraceptives, which also usually contain artificial hormones. If you think any of these could be responsible for your skin problem, then you need to address these underlying problems. You should also consider whether your make up is irritating your skin, thus causing it to darken. Once the underlying problem is addressed, your skin color will return to normal within a month or so.
