The injury that you have suffered is quite a rare one to experience, but not completely implausible; however, just to clarify, it would be the skin on your scrotum that is burnt and not your testicles. The skin of the scrotum is extremely soft and can experience overexposure to the ultraviolet rays of the sun – otherwise called sunburn.
Sunburn occurs when there is an overexposure to the harsh sun. Normally, the body is equipped to deal with a certain amount of sun exposure – or more accurately ultraviolet radiation exposure – because of our skin pigment called melanin. However, melanin is not as efficient as it should be in completely absorbing the ultraviolet radiation from the sun and what does get through this protective shield causes cellular damage. This damage, as far as the body is concerned, is a wound, and like all wounds this inflames. In extreme cases, there can also be blistering that happens to the skin. Another end result of this overexposure that you must be ready for is gradual and permanent darkening of the skin as well. This occurs through a process called melanogenesis. Melanogenesis is the natural reaction to being overexposed to ultraviolet light by the over production of melanin by the melanocyte cells.
The first thing that you have to do to treat your self is, as you correctly indicated, the application of Aloe Vera. Aloe Vera is probably nature’s most effective bandages and works by drying out on application and forming a film over the skin as it dries. In addition to this, Aloe Vera also has some antibiotic qualities. Since this application will be akin to a bandage, you would not want to moisturize the area. However, you would need to reapply the Aloe Vera every time after it gets washed off, as it would after bath. Reducing the discoloration that will occur due to the exposure can only be done after you are completely healed. This is because the skin bleaching that needs to be done will require lemon juice. Lemon juice is a rich store for vitamin C – the natural bleaching agent. However, it is not a very stable store and breaks down quickly after the fruit is cut. To overcome this effect, lemon juice has to be mixed with onion juice after squeezing and dicing an onion. This mixture should be mixed and applied to the complete genital area and allowed to stay for a few minutes.