The simplest solution is to be self-reliant. Use artificial "ice-packs", insulation, and your carry-on luggage. Do not allow protein-based drugs to go through scanning machines.
When purchased from a mail-order pharmacy, most such refrigerated medicines are shipped with "ice-packs" in a foam-insulated box. These boxes are usually too large to fit inside a carry-on bag, so buy a small foam-insulated freezer bag or foam-insulated fanny pack that is large enough to hold the "ice-packs" and your drugs. (If you cannot purchase such a container, cut down a foam-insulated box to a suitable size, and use duct tape to hold it together.) Sandwich your drugs between the "ice-packs", and put the sandwich in your small foam-insulated container. Put the container in the middle of your luggage, with clothes on all sides. (The clothes will provide additional insulation.)
Make sure that your carry-on bag satisfies the requirements of all of your airlines, and make sure to bring it onboard. Do not allow your drugs to be treated as checked baggage. Checked baggage is scanned (or even deliberately irradiated to cook anthrax). The scanners can partially cook your drugs!
If any of your airports have X-ray scanners or body-scanners, make sure that your drugs do not go through the scanners. Declare your drugs to the inspectors, and ask them to hand-inspect them. You will need to make sure that your container is easily unzipped (or the duct taped lid can easily be removed and reattached), so that your drugs can be easily inspected. Do not allow protein-based drugs to go through the scanners!