Help - recommendations for clinics / hospitals near Sorrento, Italy with X-ray

I haven't been to Sorrento, but while you are waiting for others to chime in with better information, I'll just say that twice in Europe when I have needed medical attention, my lodging place was very helpful in making recommendations and giving directions. If you are in a rental apartment with a not-so-pleasant landlord, that might not work, but it's worth a try. Also if your hotel or apartment is helpful, ask if they will call for an appointment and find directions for you.
Second, CentroPane's website looked like they are solely a diagnostic place and that is what you need right now.
Third, in regard to speaking English, if you choose a vendor that is larger than a single care provider, I bet someone there can speak enough English to get by. I wouldn't let that be the sole or determining factor. Both times I needed help, the educated medical professional spoke very good English. If you have a helpful hotel, they could ask about this when calling on your behalf.
Fourth, at the times I needed help, my medical policy here in the U.S. did not cover international travel, so I haven't had to deal with that. I did have to pay myself both times and file later for reimbursement from my travel insurance. Both providers took my credit card at the time, which I understand is not usual, so you might need to have cash if you think you will be charged.

Hopefully someone will come along with more precise and targeted information, but I thought I'd try to provide a few comforting thoughts in the meantime.

Check online for the US Consulate in Naples or the US Embassy in Rome. They should have a list of local doctors, clinics, and hospitals. You could also ask your hotel concierge for a recommendation.
As for your insurance (assuming it has out of country coverage)- be prepared to pay your medical bills in cash or credit card and then file a claim with your insurance company for reimbursement. It is unlikely that a doctor or hospital would accept a non European insurance, but it never hurts to ask.

So sorry you and your wife are having this experience, and I hope her injuries are not serious. I'm being a Monday morning quarterback, but before your next trip, you may want to research international insurance coverage, like GeoBlue for medical costs, and expatriation like Medjet. I am not endorsing those in particular, but gives you an idea of what is available. I hope you and your wife are able to enjoy the rest of your trip.

The hospital in Sorrento is here: they also have an emergency room.
https://maps.app.goo.gl/TE8o7B3YwerbHDzN6?g_st=ipc

For that kind of check that would be the first place to check.. If not the nurses, the doctors will speak some English.

The University Medical Center Federico II in Naples is probably the most prestigious in the region, it is one of the most prestigious in Italy. it’s a very large 1200 bed medical center campus, and I’m sure many doctors speak English there, but I don’t think it is necessary to go to Naples for a simple Rx check. The University hospital in Naples is below.
https://maps.app.goo.gl/vATkVgznASW79x1P8?g_st=ipc