I must bring a lot, a lot of prescription medications for my autoimmune diseases and related conditions, some of which need refrigeration. In all my 60 years of travel, and though I had my many different doctors’ paperwork ready, no one asked for them. Ever. I even had a card from my knee orthopedist about my TKR, since I always set off the metal detectors and airport security always checks me out personally. Nearly every one of my specialists said that I do not need the paperwork. I stopping bringing the prescription bottles long ago after my first overseas trip as an adult. I have not yet experienced a problem with airport security nor Customs. Nowadays, I travel with my medications stored in nifty, compact pillboxes, while my syringes are in a case with a frozen gel pack that keeps my syringes chilled for 48 hours. I use a bluetooth temperature sensor to monitor the chilled case.
I will say that the frozen gel pack meds and my syringes are often searched by the airport security. One look at the syringes, and the airport security politely zip up my medical bag.
For a recent 6-week trip, this is the pillbox that I use:
https://www.amazon.com/gp/product/B0BZPKRV4G?tag=casaivar02-20.
I had one for my prescription meds, and another for the many supplements that my rheumatologist bade me take. I liked them so much that I now use them daily at home.