I think she’s working this out in the moment. She repeats “the drink” four times and I suspect each “drink” reveals a different layer of realization. The drink is doing this to her. She’s feeling it burn. She’s realizing what it is doing to her. She, at some point, works out who gave her the drink – though she doesn’t name him and ultimately declares that she is poisoned without saying who.
I wonder, if Claudius hadn’t attempted to cover his tracks by declaring her swooning to see them bleed if she might have just quietly expired without creating too much fuss.
But she has to respond to his assertion. She has to include one last act of defiance before she departs – due to the drink? The drink. The drink!