My 12 week old female kitten’s anus is distended…what should be inside seems to be on…

For a kitten with a swollen bottom there are two things to consider. First, why is it happening? We can see this in kittens having constipation issues or with parasites sometimes as well. If a fecal sample hasn't been checked I would do so and even if it's negative, a dewormer is likely not a bad idea! If your kitten is a little constipated, softening the stool could help.

Second, this needs to be treated symptomatically like you're doing. It's really important to keep the area clean and moist. Sometimes an anti-hemorrhoid cream can help with inflammation. If it continues, I'd have her rechecked! Congrats on your new little kitten!