Can I sue a hospital if they failed to perform a test to diagnose the problem at hand?

Medical and dental malpractice claims are, by their nature, very difficult. Under California law, it is necessary, before filing suit, to obtain an affidavit from another professional, verifying that he has reviewed the medical charts and has found that there was negligence. This can cost several thousand dollars, and most attorneys expect that the client will cover this cost. Negligence could be defined as the failure to use REASONABLE care; not all bad outcomes are the result of negligence. You should also be aware that there is a cap on the amount of recovery for pain and suffering, thanks to the doctor lobby. Sometimes one has a good case theoretically, but the damages are too small to warrant a suit. For these reasons, not many lawyers handle malpractice cases. You should seek a specialist. You can contact your LOCAL bar association for a referral.

It takes the opinion of a medical expert to answer your question. Medical malpractice lawyers typically have such experts available. Consider consulting one. Good luck.

And? What damages?

You can sue, but if the PA followed protocol for other emergency room doctors in your area, you won't win. Sometimes the procedure is to make the initial analysis and then if the pain persists, do the x-ray. If that is the procedure in your area, you don't have a case.

They did not do a lot of other things. Who made you a doctor and able to make such decisions as to what are necessary? You did not say there was any consequence to the failure. You have to prove negligence, then prove damage (some genuine injury) why don't you ask your own physician. It is a medical call at this point anyway.

I do not see anything in your description that qualifies as malpractice. Many conditions could cause the symptoms you describe and their are any number of tests that could be performed. Medical science is not an exact science and from what you describe it sounds to me that the PA made a judgment call. Also, it is not clear how much worse off you are as the result of the lack of further testing.