Hi Robin,
Firstly I am sorry you are suffering from this problem, psudemonas is not a nice bacteria. Unfortunately, it is has a high
resistance to penicillins and many other anti biotics which makes it difficult to get rid of. However, some psudemonas are sensitive to piperaciliin, tobramycin, imipenem, cyprofloxacin and ticarcillin... although these are still not guaranteed to work. I don't know what anti biotics they have already tried you on, some of these may be worth a try.