Hi Ryan,
You can bring an unlimited number of unused syringes when accompanied by insulin or other injectable medication through TSA screening and onboard the aircraft. In fact, never place any medications that you cannot be without in a checked bag, it may not arrive with you at your destination!
If bringing used syringes onto the aircraft they must be in a sharps container.
As far as the medication, the pharmacy label with your name, dosing instructions, and the prescribing doctor's name that was attached to your medication when you picked up your prescription is sufficient evidence that the meds are legally yours.
If you have any questions ask me here or PM me.
Have a great trip!