Well, that is the beauty of Diabetes! You get to do what so many other healthy people would like to do but cannot or do not for fear of weight gain. But we get to have a snack!
I do understand what you feel like! I have in the past had such bad hypos that I do know that I should eat, but do not know what to eat, or even how! I do not know whether you live alone, but that does make it worse! Part of the reason you feel so scared is because one of the things that happen when you have a hypo is that your adrenilin kicks in "BIG TIME" and that makes you anxious or panicky!
Either you need to reduce your bed time insulin - I am guessing that you might be on a "human" or analogue slow acting insulin at night. Or, as your doctor says, need a snack!
I tend to have a couple of mini bars - say Snickers or similar and a handful of small crackers or chilli bites. That usually does it for me and I do not wake up high in the morning. The insulin you give yourself before bed will still be in the system and can deal with it.
I am now on Pork insulin - long story - and most of the time I do not have such a problem - except for some reason when I am staying with my mother, then I hypo far more frequently and almost guaranteed to do so at night.
It is a well known fact that the sugar levels are at their lowest at around 3 am. It might be worth setting your alarm to just before that time to check and record, for a few nights at least to see if you can work out an average.
I do not know if you are hypo aware or not. I am not. Sometimes when I wake higher than normal and I have a feeling as though I have a hangover, though I have not had anything alcoholic it is almost certain that my blood sugars dropped low, but not low enough for me to wake with it. Your body will eventually correct it and probably over compensate, causing the higher wake up readings.
I hope this helps. Let us know how you get on!