The ways of defending a speeding ticket are basically:
(1) To challenge the officer's determination of your speed. You would have to know what method the officer used to determine your speed -- like a radar gun, laser, or pacing. And then you would attack that particular method. This type of challenge can get very technical by questioning the radar gun's or laser's calibration and operation. So it is very difficult.
(2) Claiming an emergency forced you to exceed the speed limit to avoid injury to yourself or others. Unfortunately claiming that your menstrual cycle just started would unlikely be persuasive to a court. You might try to claim that because of your menstrual cycle you became unaware of your speed, but honestly I don't think it would work. If you were rushing to get to an emergency room because of some immediate medical crisis, that might work.
(3) Claiming that the officer stopped the wrong car that was speeding. If you have any evidence that the officer saw a different car speeding and stopped you instead, that could be a successful defense.
So, these are the three ways to defend a speeding ticket. In your situation, I think your best option would be to try the suggestion in #2 above, that your menstrual cycle caused you to be unaware of your speed, and if you are lucky, the judge may show leniency.