Does having an anal fissure increase chances of catching infections from toilet water splash in public bathrooms? what are names of such infections?

No.: This is not a common way to contract any infection at all. An anal fissure is internal and does not come in contact with most external sources. Toilet water itself can harbor e. coli and other colon bacteria, but these are often bacteria that already live in your gut. Anal fissures are more likely to become infected with your own fecal bacteria. If you are concerned, please see a doctor.