Do you think the medication they prescribed me is strong enough to cure my infection even with the onset of back pain?

Yes, the medication prescribed should be strong enough to cure your infection, even with a slight back pain. If you don't see significant improvement in your symptoms within 48 hours of starting the treatment, you should contact your doctor. If you develop a fever, chills, or if your symptoms worsen instead of improving, you should consult with your doctor on the same day. The treatment may need to be adjusted based on a medical examination.