You can use the gel based ice packs. they stay cold for hours. even
the small ones ( that look like a pouch) work well too.
Carry an extra icepack or two and a ziplock bag. On the flight you can
ask for exgtra ice, and let the spare icepacks stay cold. Should give you
a couple more hours of cool pack after the flights.
Its not uncommon to ask a restaurant or hotel to keep the
icepacks in the freezer for you.
If you mail-order your medication, they may even come with these
ice packs that you can reuse.