Final answer:
Escherichia coli (E. coli) is the most likely causative agent of the urinary tract infection in the 22-year-old woman due to the presence of gram-negative rods in the urine culture and E. coli's frequency as a UTI pathogen. Nitrites in the urine further support this diagnosis.
Step-by-step explanation:
The etiological agent that is most likely responsible for the urinary tract infection (UTI) in a 22-year-old woman presenting with frequent and painful urination and who has cultured gram-negative rods from her urine is Escherichia coli (E. coli).
Gram-negative bacteria such as E. coli, Proteus vulgaris, Pseudomonas aeruginosa, and Klebsiella pneumoniae cause most bladder infections. In this case, given that gram-negative rods were identified and E. coli is the most common cause of UTIs, it is the probable pathogen. Moreover, the presence of nitrites in the urine would support this diagnosis as E. coli produces nitrate reductase which converts nitrate to nitrite. Mycoplasma hominis is typically associated with nongonococcal urethritis rather than UTIs.
Treatment involves the prescription of antibiotics, and while ciprofloxacin is commonly used, it is important to conduct antimicrobial susceptibility testing to ensure the effectiveness of the antibiotic against the specific strain of E. coli identified.