Almost everyone has certain habits, some bad, and even the good habits in excess can sometimes be annoying to observers. Some of these habits unchecked can lead to habitual addictions. But you need to understand that addiction isn't the point of worry, the actual problem lies with the object, behavior or substance addicted to.
Menthol is an organic compound, synthetically made from mints like corn, but mostly obtained from oil mints.
On the good side, menthol gives a soothing feeling on the body senses. Menthol in peppermint tea helps to aid digestion, reduces pain, and eliminates inflamation thereby relaxing the body. That's when if you take it in the right doses. But from your narration in the question above, I think you're very well going over the safety dosage boundary.
Am not a health expert, but am made to understand that consumption of menthol in excess usually above 20ml can lead to certain health risk and overdose. Some of the effects experienced which may very well lead to an overdose are abdominal pain, skin rash, dizziness, nausea, vomiting, etc. These are abnormal negative body effects that a healthy person shouldn't be experiencing. If you feel any of these effects, I suggest you dessit from taking it and visit your doctor.