Today it's raining over here..!!!

Today light drizzle of rain took place over here...!!

drizzle means light rain so using light and shower is not possible.

Today it's raining over here..!!!

Today light drizzle of rain showers took place over here...!!

you can use both in conversation, Drizzle and showers, it may seem redundant to some but, but is not confusing, and could be common conversation english where I added in rain is unnecessary

Today light drizzle of rain showers took place, (where I am located at specific location, would be better then here or over here)