Made up rule number 678. The "just for next time" was the choice of wording to prevent loss of face.
It is extremely important that syringes are carried securely and safely. Plus being carried next to a human body at 37 Celsius is unlikely to be a good idea for the medicines in question. It does make sense to travel with a bag which is easy to put in an overhead, not too big and which secures syringes and sharps properly, so that may be one thing to think about.