Yep, you've been drawing all those cards for nothing.
According to UNO, there's no need to draw countless cards until you get a colour or number that matches the Discard pile. You only have to draw ONE, and skip your turn if you can't play that card.
To add insult to injury, we regret to inform you that it's stated in black and white on the card game's official instructions. It reads:
"If you don’t have a card that matches the one on the DISCARD pile, you must take a card from the DRAW pile.
If the card you picked up can be played, you are free to put it down in the same turn. Otherwise, play moves on to the next person in turn."
But here's the kicker - the "rule" does not apply for UNO's PC, console, and mobile versions!
Now if you'll excuse us, we're gonna continue watching our opponents sweat as they keep drawing cards because they don't have a card to play. :p