Why am I not getting job offers? I have one thought--I haven't worked in 3 years due to an accident. The resume shows short-term positions, some of which were per diem. How can I change my resume and cover letters so that there is not blaring gaps.

I would start my stating how long you have been a Nurse and what type or occupation you have trained. Example I have been a Registered Nurse for the past 8 years working in BH/Substance and Alcohol abuse in Outpatient facilities or Clinics.
Then state you are looking for another part time or per Diem position. You just want your foot in the door.
Then I would list my experience in bullet points with the number of years. Example, Triage 1 year,
Documentation 3 years,etc.
After that I would list my positions I held and the number of years at each facility.

Highlight your relevant experiences and when asked about the gaps, be prepared to answer honestly. It may also help to briefly address the gap in your cover letter and what you did during that time including efforts to maintain your competence such as keeping your professional certifications current and completing your required continuing education activities.