I don't know about hypoglycemia, I've never heard that it has anything to do with animal protein. However in my experience people who say vegetarianism has made them ill tend to either have very poor diets (and therefore it isn't vegetarianism but a poor diet in general), or it is simply in their minds. I've heard many people who haven't eaten meat for a matter of days - or even hours - claiming to feel a whole host of ailments, usually including weakness, dizzyness and tiredness, that magically dissapear as soon as they eat a hamburger.
Excuse my scepticism, I am sure there are some people who for health reasons cannot - or find it difficult to - be vegetarian. Infact I've known people with digestive problems meaning they cannot eat beans, legumes or tofu which would certainly make maintaining a healthy vegan diet quite difficult. I'm also sure some people develop health problems that dissapear when they eat meat again, for example I know people who suffered with anemia and stopped being vegetarian and got better, however they would also have got better if they had eaten other vegetarian foods that would have improved their iron intake - the problem was they stopped eating meat and didn't replace it with anything! (ie: just eating carbs and veg).
Anyway for your friend I'd advise she goes to the doctor - a few months is a long time so it seems unlikley its psychosematic, it could be unrelated to diet, and if it isn't her doctor can find exactly what it is she's missing out on, and then she can work out what vegetarian foods she can eat more regualrly to help (and her doctor may also give other help depending of course).