If you are flying, you will want to be aware of how to best get liquid medicine, in particular, through security screening processes. You will also want to pack any critical medicines in your carry on so they are handy during flight.
The TSA site has a lot of good advice here: https://www.tsa.gov/blog/2014/09/05/tsa-travel-tips-traveling-medication
The CDC site has some advice on what to include in your travel health kit here: https://wwwnc.cdc.gov/travel/page/pack-smart
For driving trips, we also heard some advice on purchasing a cooler that is powered by your cigarette lighter or USB-powered to keep any necessary medicines cold. Here’s one example – https://www.amazon.com/NutriChef-Portable-Electric-Thermoelectric-Refrigerator/dp/B06ZXZ7PDC/ref=sr_1_11?ie=UTF8&qid=1525730407&sr=8-11&keywords=best+travel+cooler