I'd say that the antibiotics are a culprit if they make her drink more water. You may want to double check with the vet on this. Why is she on antibiotics?
Once they've pee'd somewhere like the blanket or bed, they are likely to go back there. I would agree with washing them pronto, then be very diligent about taking her out more often. (And I know how hard that is to do.)
If you can catch her in the act I would say a firm "No" then take her outside to the area where she usually does her business. And if she's already sprinkled on the blanket it's back to the washer!
I'm no expert here - just a suggestion.
RIP Wallis, John Robert, Tibby & Pip
Mom to JoJo, Roxie & Linguini (Cavaliers)
and my birds Moji (Senegal) and Walter (Blue Front Amazon)