Yes it can appear only on one side. You can get it on other places in the private area, and you can also get it in the mouth.
It actually hasn't appeared from nowhere. It has probably been manifesting itself slowly that you were not aware of to being with.
Don't use any soaps or shower gels down below, this can aggravate the skin.
would it just appear out of nowhere and only on one side?
This is likely to be Thrush. Thrush is a fungus and likes areas where it is warm and moist. We have Candida Albicans on our body, and when this gets out of hand due to bad diet, too much sugar, not controlling diabetes, through antibiotics, as well as through having sex we start to get the red burning or itching symptoms.
Keep the area clean, wear cotton under garments, not tight clothing.
Get a prescription to treat fungal problems like Canesten or Canesten HC, Trimovate. Your doctor or pharmacist may have other antifungal creams available without prescription.
Natural yogurt applied to the area will help. As well as dring natural live yougurt to get your body flora back to normal.