I think you probably could do with antibodies and c-peptide tests. Antibodies testing may or may not pick up an issue. C-peptide will give an indication of how much insulin your body is producing (aim to have blood glucose of around 7mmol/l for the test).
If you are type 1 you will require insulin.
With LADA the rate of destruction of beta cells varies with some having to start on insulin relatively quickly while others may not get to the point of requiring insulin.
Suggest you get the testing so the most appropriate treatment can be established.
You are clearly still at a point where your body is producing some insulin otherwise you would not get a blood glucose reading of 3.9 mmol/l.