If you are a type 2, going on insulin doesn't make you type 1, it makes you someone with type 2 diabetes who is on insulin.
It looks like you are getting to grips with the insulin well. Remember that you can contact the clinic for further support if you need it. Even if you just want a recap of why you have been discharged, who you should contact if you need more help and anything you should be mindful of in managing your diabetes on insulin, it's fine to contact the clinic to ask