There are a lot more types of diabetes out there other than T1/LADA and T2, but T2 seems to be the catch all definition that gets applied when another type can't be assigned.
There are many different types of diabetes resulting from various causes. The table below provides a basic classification by aetioloigy (cause). Please do bear in mind that as our knowledge and understanding of the interplay between genetics, environment and health continues to evolve, so does...
eg has your consultant considered T3c and MODY????
Some people never find out their specific type but just have to find a treatment that works for them....