What insulin are you using?
If it's lantus or Levimer then this is a background insulin, which is normally a evening injection, but it is timed so if you injected at 9pm then you should inject it at 9pm every night...
Just because you've started using insulin doesn't automatically change your status, you become a T2 taking insulin...
You do need to ask your DSN, why you've been changed to insulin, and why such a small dose, 2unit's of insulin for somebody who's supposed to be T2 insulin resistant is a rather unusual indeed..