I would get a Frio.
http://coolerconcept.com/
I have several different sizes. I am a diabetic and use it for my insulin while traveling. You don't need a fridge or ice packs. Just soack it in cool water for a few minutes and it will keep your meds cool for a whole day. You can slip it into your carry on, no big deal.
You might, if it makes you feel better, call the airlines and ask them.
I have never had any problems with my insulin and syringes at the airport.
Take you prescription pable with you so security can see that you have to have it.

You have to get a paper from the doctor for the shots but not the riba, have the perscription bother for the pills, I flew all the time, they never asked but if I didnt have the paper they would, lol, I called the airlines and they informed me.

typo (bottle)

I traveled Northwest this summer with my epi pin for Hep C. The dr. did say to use a cooler and Ice pack. I didn't have a problem. I actually brought what I needed in the perscription box.

I've done it a couple of times. It's no big deal. Having the doctor's note handy is not a bad idea. Trap is right, soak a facecloth and stick it in a bag and wrap it around your junk. Stays cool and the box doesn't melt.

i took intron thru the airport without so much as a glance. and im the guy who crank calls the dc drug information hotline to inquire as to the wherebouts of some hashish. i had a deputy friend pull me over once asking me where the crank was coming from. im gonna pull him over some day and ask him wheres the hash. fairs fair..once the lawman brought me a half gallon of confiscated moonshine. he took it from a thug and gave it to a hardworking citizen. yup hes my buddy. :)>