I agree with everyone that you should take your syringes in your carry-on. They are considered medical supplies and don't count in your carry-on total. Since I have an entire bag devoted to just medications(sigh), I usually end up with two carry-ons.
You won't need a prescription from your doctor, but the medication should have a pharmacy label on it. I also carry a letter listing my medications that my physician wrote out for me. I've been asked for it one time and have been told it is not usually asked for on domestic flights, but is a necessity for out of the country flights. On the same flight I was asked for the letter, I was also told initially that the syringes would have to be checked because I was required to have a sharps container with me and if I didn't have a way to dispose of the syringes on the plane, they couldn't come on the plane with me.
Now, all of us who use sharps containers KNOW how big they are and how much of a pain it would be to travel with them. But I had been warned about this on one of my other boards, and since I had needed to get a medication carrier that holds a cold pack, when I bought it I made sure it had a "medical waste" pouch. Which is basically a stiff plastic zippered "bag" with the words "medical waste" printed on the side.
Oh, and you can dispose of used syringes at the First Aid Stations in the parks. And keep medications refrigerated there too. Plus they have insulin syringes if you need one because you ran out and don't want to have to go back to the room for more.