One thing I would find out is the culture sensitivity. What this means is finding out of the bacteria causing the infection is sensitive or resistant to the antibiotics you were given. If the bacteria is resistant, then the infection isn't appropriately treated. In this case, then it is possible to have the infection while on antibiotics.
I would also consider a kidney ultrasound to ensure there hasn't been any anatomical damage to the kidneys.
If the urine continues to be cloudy - I would re-analyze the urine for infection via urinalysis, and consider a more extended course of antibiotics. A urology referral may be considered for further evaluation.
As for your question - the way to determine what cells is in the urine would be via a urinalyis. It is possible that epithelial cells (sloughed cells) may be present.
Followup with your personal physician is essential.
This answer is not intended as and does not substitute for medical advice - the information presented is for patient education only. Please see your personal physician for further evaluation of your individual case.
Thanks,
Kevin, M.D.