You can keep your insulin cool with a Frio pack. It uses evaporative cooling and works really well. I got mine on the web not sure if you can find one locally on such short notice, but you'll what to get one when you get home.
Any airlines I've flown have no problem with syringes/needles/insulin. I usually send them through in my carry on and haven't had anyone take notice. Most will allow you an extra carry-on for medical supplies as well.
I wear my Medical Alert 24/7 - don't always feel my hypos, and I think better safe than sorry :)
Hope you had a good trip! I second the Frio, great piece of gear.
I have flown internationally with insulin, syringes and pens without issue. To be totally safe, have a doctors prescription for all the items (even the syringes) and you should have no issue. Security may examine your medication and make sure it has your name on it, and in the most extreme case ask you to prove you have a prescription. I have had security look at my diabetes supplies and once or twice asked if it was mine, but I have never had them actually look for my name on the insulin or ask me to show my prescription and I've flown about 50 times since starting insulin.
You should always carry a note from your doctor explaining what supplies you need to have with you. The note should cover that you require not only syringes and insulin, but also juice, snacks, and other fast-acting carbs in case you go low. Make sure to keep ALL your supplies with you at all times (never check them in your luggage).
It is definitely a good idea to wear some sort of ID noting that you're diabetic. I also sometimes alert a flight attendant on long flights, just letting him/her know that if I ask for juice, it's because I'm going low and it could turn into an emergency and I might not be able to explain coherently why I need it (I had a bad experience once where I asked for juice, but could not articulate that I was low, and the flight attendant just thought I was being a demanding passenger).
Frio pouches work well for keeping insulin cool, but if you're not planning on being out in the heat for long periods of time, your insulin should be fine not in any cooling container. Just keep an eye on it and make sure it's not exposed to any extreme temps. that said, I LOVE my Frio pouches.
You should use caution with the use of freezer packs or ice packs with insulin. While they can be used to keep things cool, if insulin is in too close a contact it may get too cold. Insulin at room temperature is fine for a whole month. Unless you actually think you will stuck out on the runway in hot weather, you should actually be able to just pack it in your carry on and it will be fine.
You can also wrap the insulin in a few layers of towel and put them in with an ice pack if it makes you more comfortable. No, I don't think you need to take all the syringes in the cabin, but take at least twice what you think you will need in your carry-on. Don't forget some glucose tabs, skittles... something with fast-acting carbs just in case you go low. It's best to have the prescription label with your name, etc. on the insulin if possible.
I have a basic rule I apply when deciding whether to put things in checked or carry-on baggage.
If I cannot accept loss of that checked baggage when I arrive at my destination, then it goes in my carry-on. If that the item would not get through security in the carry-on, then I do not take it. No exceptions.
I work on the presumption that the chances of myself and my checked bags arriving at my destination at the same time are more a matter of luck than good management. Of course, if it was really important, you may be able to buy it back here: Unclaimed Baggage Center.
Do some reading about the size of that place and how much it holds. Scary, but educational.