We have a good example of different practices running along different guidelines. That is the airlines, the airport security, hospitals and GPs. Regarding the airlines and the airport securities - they make the rules up as they go along. It depends on who you are, where you are boarding, and what you know. The complications are understandable, but annoying.
Different countries have different rules. In the USA diabetes is treated across the counter at the pharmacy. I used to get my medication direct, and no doctor involved. They are very laid back about it. In the UK, and Europe, that is not the case. I have never had problems with insulin, pens and needles on entry to the US, or in South America. I have never had problem in any UK airport - LHR. LGW, EDN or LUT.
I had difficulty once in Paris - they were tent screening for drugs (1972), and I had some idiot accusing me of drug addiction. I laughed at him, and said he was ignorant, and requested someone who knew what they were about. He got a senior, who also laughed, and apologized to me. The more worrying case was in Athens in 2006. A BA check in girl had problems, and caused a scene. I told her to calm down, and told her that my medication was private to me, and not up for heated discussion. I then reminded her that it was up to the pilot to make the final decision. She contacted the seniors, and in a few minutes I was allowed checkin.
I have noticed that airports are now demanding passengers put all medicines in plastic bags, and carry them openly. So far I have never done this. I put all my medicines in plastic bags, but keep them safe in my hand luggage, out of view of other passengers. My luggage is frequently checked through security, and I tell them what it is, and that I do not like publicly displaying it. No security officer has ever taken issue with that.
I always take diabetic validation - like a diabetic card, and a prescription form with me. I hold those in my wallet all the time - a sensible procedure. I also ensure I know the terms in the language I am visiting. I always prepare a card stating my medical condition, and what to do in the case of a hypo - viz sugar, in the language of the country I am visiting. I also make sure I know the words for sugar, without sugar, insulin, diabetic. That seems fairly easy and sensible.
Hope this helps.