Would I get infected if contaminated water splash up to my vagina from public toilet?

Always flush toilet. Possible, but unlilkely. Also could depend on what contaminates the water. Remember, the water that flushes toilets is the same as drinking water, so always flush before sitting. Sometimes there are cleaners in the water that could cause some burning. To be absolutely safe, stand before flushing and if a question use sink water, wet some toilet paper and gently clean yourself off.