Most shooting stars are the size of a grain of sand and whilst specific meteor showers happen at certain times of year, meteors hit the earth all the time - there is just a greater abundance of them at the times of showers.
This ISS (and shuttle and Soyuz) have shielding in mind for these micrometorites. Doing a search on that term should bring up a wealth of information. In short, micrometeorites pose a known risk. Meteor showers raise this slightly but it's not a major concern.