I briefly met someone who had very similar reactions to Levemir - he was one of the guys who was on the same carb counting course I went to about 2 years ago (it was every Monday for 4 weeks), he was pretty newly diagnosed, just after the 2nd week of the course he spoke to the people who were running the course (before then I don't think he realised that the levemir could cause that so hadn't said anything) and they got his levemir changed to something else and on that 3rd week he was overjoyed at how much better he felt, so yes it is quite possible.