Final answer:
The most likely diagnosis is acute cystitis, a bacterial infection of the bladder. The urinalysis findings indicate an active bacterial infection and previous treatment with trimethoprim-sulfamethoxazole and nitrofurantoin both were effective.
Step-by-step explanation:
The most likely diagnosis for the 30-year-old woman with urinary frequency and pain with urination is acute cystitis. Acute cystitis is a bacterial infection of the bladder, which commonly occurs when bacteria from the lower gastrointestinal tract enter the urinary tract. The presence of greater than 20 white blood cells per high-power field and 3+ bacteria in the urinalysis indicates an active bacterial infection.
Escherichia coli is the most common bacteria associated with cystitis, and the sensitivity of the urine cultures to trimethoprim-sulfamethoxazole and nitrofurantoin suggests that these antibiotics were effective in treating the previous episodes. The patient's symptoms and urine analysis findings are consistent with acute cystitis, and further treatment with appropriate antibiotics is recommended.