I had never heard the adjective irritative before. As Lisa says, it mostly seems to be used in medical contexts - it certainly seems to refer to physical irritation (I imagine that certain plants which make you itchy when you come into contact with them would be described as "irritative), whereas "irritating" seems to be more linked to behavioral contexts, with a meaning similar to "annoying".

They're basically the same thing, though I've rarely heard anyone use irritative. In fact, I looked it up to make sure it's a real word -- and I'm a native speaker. It looks like irritative is used mostly in medicine. An annoying little brother, an eyelash that got in my eye, an extra-long wait for the bus -- those are all irritating. At least in American English, you should be fine using just the word irritating.