Cats tend to do this if they are ill. I see that your kitty had a bladder infection and was put on antibiotics. I'm assuming the cat was re-tested for the infection after the antibiotics finished? (If not, you should have her checked again since sometimes antibiotics are not successful the first time around.) Also, cats her age frequently begin to have kidney problems, so it might be good to get her checked for this. You should also have her tested for diabetes, especially if your cats eat dry food only. Is she drinking more water than usual?
Assuming your kitty doesn't still have any traces of infection, and that her kidneys are okay, the problem for her is that she now associates the litter box with pain (the burning feeling she had when she had the infection). What you need to do is re-train her to associate the box with pleasure. So, if you see her going toward a spot outside the box and looking like she is going to pee, quickly scoop her up and put her in the box (this is what the mother cat did to train her as a baby!). Then, if she goes in the box, give her a treat. Do that as often as you can, and hopefully she will start using it again on her own.
As your vet said, do not change the litter. Doing that often makes these problems worse. Also, make sure you not cleaning up the places she is peeing with ammonia. Ammonia smells like another cat's pee to her, and she will then re-pee on the spot to cover up that smell. What you should buy to clean the pee up is called "Urine Off" (comes in a large grey bottle with a pic of cat on it). This stuff will get all traces of the pee smell out, AND replace the smell with an (undetectable to humans) scent that the cat doesn't like, thus discouraging her from peeing there again.
Hopefully things start going better for your kitty!