That's EXACTLY what happened to me. Don't let it worry you too much, it WILL get better, so keep going!What's up with "normal" BG feeling so bad?
When I first started exercising I'd experience hypo-like symptoms in the "normal" BG ranges too, and I think it was just because my body was used to being high all the time. At diagnosis my fasting BG was 14.8 (267) and my A1c was 12.1%, so I must have been "used" to being high.
It took about 3 weeks to get more accustomed to the lower BG's from exercising. Now I don't feel 'hypo-like' symptoms until I'm under 4.5 (81).
Keep at it, and your body will not only get used to it, but the improved BG's from regular exercise is a GREAT thing.