As someone who has been on insulin for over 50 years, and who planned/taught diabetes modules to nurses, I can only tell you about my experiences or what I read/heard from Hospital Consultants.
For many years people on insulin were asked to keep their BS between 3 and 5 mmol/l which caused a lot of problems. I managed this but through what is now thought to be too low a levels, I lost my warning signs of hypoglycaemia. The only signs that I got were great weariness (putting one foot in front of another took great effort) and nausea, at this point my BS was 1.8 mmol/l or below. In order to bring awareness back, I had to live with levels of between 7 and 10 mmoll for 4 months. I now have awareness at about 3.4 mmol/l which is really too low.
With reference to brain function. The brain does not need insulin to take in glucose for energy, it can use glucose without insulin as can muscle cells, but what the brain does need is a constant supply of glucose. Lack of glucose for the brain means the brain cannot function properly while the BS is low. So when borderline - between 3 and 4 mmol/l this may affect people's ability to think, plan etc and certainly can affect mood. People describe different effects on mood, depression, bad temper, hysteria etc Below 3 mmol/l is dangerous and can lead to coma - so low BS MUST have an effect on brain function if you think about it.
Lack of brain function may also explain why some people have strange dreams/nightmares/illusions during severe hypoglycaemia. I once refused sugar in my coffee - "because that sugar was the wrong sort", luckily I found the "right sort" in a nearby office!!
So a low blood glucose definitely affects brain function, whether or not the brain cells can be permanently damaged is difficult to assess. It would require people having a base line brain scan, then ones at intervals every time they had a hypo. It would not be ethically sound to induce hypos to see the effect. The only other way to assess the effect is to take histories and ask people what their opinion is if they have had numerous hypos. All I know is that after a severe hypo, before people realise I had lost awareness, I lost the ability to remember names of places and people, including family members. I had a photographic memory before and the problems developed immediately afterwards. That happened in my 40s, I am now in my 60s, and the problem persists.
Incidentally, this can be a problem for people using insulin during exams and other times that require increased brain function. The brain uses up glucose at a rapid rate without utilising insulin - which can lead to a hypoglycaemic attack. Which is one of the reasons being a "good little diabetic" with perfect BS levels and HbA1c is so difficult.
So you need help to get your BS under control and to avoid hypoglycaemia. A diabetic nurse specialist, who has been educated in insulin prescribing (not all have) is what you need. It will not happen overnight that you become stable, it takes time, effort and frequent contact at first. You need to record insulin dosage, site of administration and what happened before hypos to help in detecting a pattern, if one exists.
I hope that helps a little, insulin therapy is not easy, do not let anyone tell you it is. I have found it easier since I retired as my days can be similar in times of eating, exercising etc. But for teenagers, people who work, parents bringing up a family etc it can be very very difficult as no day is the same.
Liz