A urine sample can usually still be given during your period, though the blood in it can interfere with the microscopy and culture reading. Collecting it before you start the antibiotics is usually better, since medicines already in your system can suppress the bacterial growth the culture needs to detect.
Next Steps
Ask your lab about a clean-catch technique for collecting during your period, and check with your prescribing doctor whether the antibiotics should wait until after the sample is given. Your current urine tests screen for a bacterial UTI, not STIs, so ask separately for chlamydia or gonorrhea testing if that worries you.
Health Tips
Whether to start or delay the antibiotics is best decided by the doctor who prescribed them, since only they have your full picture.