Had this exact same problem about a month ago.
You're right, it's most likely the motor mounts.
From doing research here and elsewhere, you really need to spend the money on the dealer part rather than the autozone equivalent, as they tend to only last about six months for some reason.
There are three, Passenger side, "dogbone" on the drivers, and transmission.
It's been suggested that you replace them all at once to keep the old ones from letting the new one take a beating.