Thank you for asking your query at DoctorSpring.
Your Doctor has prescribed an antibiotic of the Quinolone class – Ciprofloxacin. Since you are having nausea, dizziness and drowsiness after taking the drug, it’s possibly a drug side effect. These are one of the most common reported side effects of the drug. But there is nothing to be alarmed of. You can take the drug with food to avoid stomach upset. Drink plenty of water. Lie down if you feel more dizziness.
Still if the discomfort is persisting I would recommend you to report it to your Doctor. Prostatitis will need prolonged duration of antibiotics than usual, so it will be prudent to switch to another antibiotic if the side effects persist. There are enough choices available in that regard. Your Doctor may carry out some more tests to aid in the diagnosis of the etiology (ie to find out which bacterium is causing it).
Hope this helps