A cure for sunburn should have an anti-inflammatory effect, or a soothing effect on the skin. Out of the two items that you did describe only yoghurt sounds like a candidate and that too for the soothing effect. If you are looking at a healing effect, then what you should be looking for is some kind of a bandage for the skin. Sunburn is a kind of injury that will heal in its own time, so there is precious little that can be done to cure the condition as such. You will have to give the skin its own time to heal. When you get sunburned, the skin gets inflamed and turns bright red in color. The only way to rectify this situation is to use an anti-inflammatory cream. If you were seeking a medical remedy, a doctor would probably prescribe something like hydrocortisone cream to calm the inflammation. However, this is a double edged sword. This is because hydrocortisone is a corticosteroid cream and this works by suppressing the immune system wherever it is applied. This can have serious effects like allowing a bacterial infection to suddenly take a vigorous hold. Therefore, it is better to stick to an herbal remedy.
When the skin is exposed to ultraviolet radiation from the sun, it gets damaged at a cellular level. This can be a problem for light-skinned people because of a lack of protective melanin in the skin. Darker-skinned people are also prone to sunburn but they can tolerate the sun for longer. When there is a massive amount of cellular damage in the skin, the body’s immune system kicks in and causes an inflammation, one of the signs of which, is the redness and blisters that occur after sunburn. This reaction is necessary as the dead and damaged cells are killed off by the white blood cells, and replaced by proper healthy cells below. However, as with all inflammations, this one is painful.
What you need to do is to moderate the immune system response and cover the skin from any source of infection. Whenever the pain of the sunburn is too much, run an ice cube over the skin. This is the general rule in all painful inflammations and is called a cold compress. Use this only when you can’t take the pain. After this, you need a skin bandage, which can be found in aloe vera. Aloe vera dries up on the skin as soon as it is applied and seals it off – effectively becoming a bandage.