It would be relatively easy for your doctor to order a few antibody tests. For reasons I fail to understand, many doctors are reluctant to do this. Check out @Melitta’s informative post on these tests.
Testing for MODY involves genetic analysis, is very expensive, and is not often covered by insurance. Therefore, I think doing the antibody tests and if you came up positive then you could conclude that you have autoimmune diabetes, the LADA form of T1D.