I disagree with the ones saying that this is too powerful, your damage is COMPLETELY up to the opponent, you cannot damage them unless they allow you to, by playing quick cards, they can see your hand afterall.
The only way you can "surprise" them with it, is to play quick/swift cards of your own, in which case, you'll be taking the damage as well, another balancing factor.
Also, the opponent can always discard (either the discard function, or the many many cards that allow you to discard cards) You wanted a serious downfall to playing so many quick cards, here's an example of that, it's not overpowered, as all the damage you do the opponent is completely up to them.