You can take it on your flight. I've taken insulin on every flight, over 50 flights, including overseas. With all the major airlines Never had it questioned by TSA. They got though the scanner. I keep them in one carry-on.
Confirm with the airline before hand
the folks that answered your question are correct. Inform the TSA agent that you carry an insulin kit w/needles. They will let you through. Recommend you access your airline's website as each airline have different rules.
You have to show them, and carry it on. A guy in front of me went through the same thing. It does need identified.
Does it have to have a prescription label on the insulin pens? Or is the medication label enough?
Your allowed 1 carry on and 1 personal item. Have. Your medical in a bag by itself and tell TSA what it is.
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