Hi Mary,
Sorry to hear of your troubles. As some have already alluded to, exercise can have strange effects on BG levels. Initially when you perform a decent intesity of exercise, your BG will actually raise slightly. If you are already a bit high (>12ish) it can raise substantially, initially.
Exercise OVERALL has the effect to reduce BG independet of insulin. This is because generally skeletal muscle cells upregulate the glucose transport molecules to the surface of their cells so glucose can be taken out of the blood, into the cell, thus lowering BG. Insulin is usually required for this, but a separate pathway for this occurs with exercise.
The key to understanding the implications as a diabetic, is not the science behind it, but simply that insulin (well, normal insulin i.e. fast acting) happens rapidly in a nice short peak. So you take insulin, or pancreas produces it, and it quickly shuttles in glucose to your cells. Exercise however should be considered more like a long acting insulin. The effects of exercise take a little while to occur in terms of blood glucose lowering, but when they do, they do it slowly and normally noticably a number of hours after exercise. So for example if you exercise at 7pm for 1hr, your BG will be at its lowest probably around 11pm-2am.
As you get older as well, and metabolism and fat levels change in the body, this process can slow down and be less as effective. All things to bear in mind.
This would explain why initially you see a rise in BG, then later get a hypo. Really if you are going to exercise, you should try and ensure 1-2hrs before that your BG is <10 ideally.
For me, I exercise twice a day on weekdays, 6:30-8am in the mornings, then 12:30-1:15 or so in the afternoons with a run, and on those days I can keep my levels between 5-7 with a good diet and NO novorapid, just lantis/glargine (basal bolus) injections.
Hope this helps!
J