Positive ketones in urine suggest absolute deficiency of endogenous (from your body itself) at that point of time and one should take insulin as treatment. This may indirectly suggest type of diabetes as positive ketones suggests diagnosis of type I diabetes. All type 1 DM need insulin for treatment. The confirmative test for type 1 DM is antibody test in blood. When insulin is given ketones disappear quickly in a few hours only. Advice not to exercise is given for that short time only.
Coming to your case, urine ketones as trace have no meaning. Your blood glucose levels are not too high to take insulin and medication (diapride). By now your blood glucose must have come down and in my opinion you can have a good control with oral medications only. If you have no heart problem (clearance from a physician) then you can go ahead with muscle strengthening exercise. For diabetes control 30 metres daily brisk walk/jogging is good enough.