Hello and Thank You for contacting JustAnswer
I am sorry your little one is having trouble. I too am owned by a shih-tzu so it breaks my heart when these little ones have trouble.
Pseudomonas Aeruginosis is a very rare type of bacteria and can be very resistant to medication. Often we treat this for 7-14 days and the problem seem to clear only to develop again even more resist to antibiotics.
Cipro and Enrofloxacin are the most common drugs used to treat this infection if you are taking a break in between rounds of antibiotics you may need to try 3-5 weeks of continued antibiotics with out a break in between.In most case a antibacterial shampoo is also recommended. If you have not be using a wash I would suggest asking your vet which wash would be best.
Here is some additional information
Ones study done on dogs with this problem says that as long as 12 weeks of antibiotic treatment may be needed.
This study also reveled that many of these dogs also have Folliculitis which is a skin condition that causes itchiness, hair loss and pustules on the skin's surface and is a result of a staph infection of the skin.Some dogs were also found to have furunculosis.
Here is this study
In some dogs topical silver sulfadiazine cream is helpful
Until you can see the vet again you can purchase antibacterial shampoo at your local pet store or in a pinch antibacterial liquid soap such as dial can be used.
Over the counter benadryl may also be helpful for the itching. This is normally dosed at 1-2mgs per pound of body weight every 8-10 hours as needed.
I hope this has been helpful,please reply back if you have additional questions or concerns