OEM motorcycle tires are usually pretty soft right from the start, especially on sporty models like the YZF. Three months is really not much time, so the quick wear could be coming from a few different things. First, check if your tire pressure isn't too low - an underinflated tire wears much faster and unevenly. Second, if you're doing a lot of tight cornering or leaning hard, the tire wears faster because the rubber is constantly working at that limit. How you brake matters quite a bit too - if you're locking up the tire a lot, it's going to wear down quicker.
As for switching brands, Michelin and Continental are solid names, but the brand isn't really what matters most. The tire type is more important - if you've got soft OEM tires (which come that way from the factory because the bike gets better grip), any harder tire will last longer, but you might lose some grip in the corners. It comes down to this: do you need a tire that lasts longer or one with better performance? There are middle-ground tires that balance both pretty well, like the Michelin Pilot or Continental ContiSportAttack.
My suggestion is to try changing how you ride first. Whether it's pressure, braking, or too much cornering - that makes a real difference. Then when you do buy new tires, ask for recommendations on the motorcycle forum for your specific model - there's always people who've tested different setups and know what works best for the YZF.