inundate
To overwhelm someone with too much at once.
To inundate means to overwhelm with a massive amount of something, like being flooded or buried. The word originally described actual flooding: when heavy rains inundate a town, water pours in faster than it can drain away, covering streets and filling basements.
Today we use inundate for any situation where too much of something arrives too fast to handle. A teacher might feel inundated by emails from parents, students, and administrators, all arriving faster than she can respond. A popular bakery might be inundated with orders during the holidays, receiving more requests than it can possibly fill.
The feeling of being inundated captures that sense of being swamped or buried, when things keep piling up faster than you can deal with them. If you have five homework assignments, that's just busy. But if every teacher assigns a major project in the same week, plus your inbox fills with messages about three different activities, and your coach adds extra practices, you might feel truly inundated. The key is the relentless pace: more keeps arriving before you can handle what's already there.