Hello, and thanks for requesting me.
Sorry for the delay in getting back to you, I am in a very different time zone to you and have just come online first thing this morning and found your question. My name is***** I am an experienced small animal veterinary surgeon and I will be very pleased to work with you today and will try my best to answer your question to your satisfaction.
1. This is a very short answer I know, but in my experience it can often take three or four days for a cat in your one's situation to start to respond to antibiotics. If antibiotic therapy is going to help then you can reasonably hope to start to see signs of improvement over the next couple of days.
2. In any case your vet is taking a very thorough approach in having run a culture lab test, hopefully this will reveal the cause of your cat's infection and the correct antibiotic to use, so you have this to fall back on.
3. The good thing here is that urinary tract infections in female cats are rarely very serious in my experience and usually respond well to treatment and the condition may well resolve on it's own. In your case this could well be a bacterial infection but this not so common, most female cats which present with UTI type symptoms have an inflammation of the bladder which is not infection related, but read more of this HERE
I hope I have covered your question fully enough but if you would like further clarification or to talk things over a bit more then I will be on-line for the next hour or so and I will be more than pleased to continue working with you.
Please be kind enough to rate my service to you after we have concluded our dialogue, such feedback helps me maintain the quality of my answers.