If you are likely to carry strong medication with you, keep the bottles that the medicine came in. If it is prescribed it will have your name on the bottle. Also get a note from your doctor saying you need to carry the particular medication due to a medical condition.
Just because you change time zones doesn't mean you have to change your medication schedule. Instead of struggling with any confusing adjustments, bring an extra watch set to the time zone where you live. That way, you can take your medicine at familiar times without any problems.