A UTI is very uncomfortable and even can be very painful for human or animal. I had one personally myself and it was quite miserable and cannot imagine a puppy having one for a month without treatment. It's the kidneys that is affected from a bladder infection which can back up into the kidneys and cause failure and even death.
Why did this go on for a month. The vet could've tested both the pups urine to determine which one had the uti. A uti can travel to the kidneys and can eventually lead to kidney. Failure or even death. The poor pup will be in agony and this has been for a month??? My god.
Be prepared for blood work and urinalysis and you will get all the answers you want...
Your vet will be able to answer all your questions about your dog's health. Please take her in ASAP -- bladder infections are *painful*!
More likely, kidney problems.