Latent Autoimmune Diabetes Questions

I am an active, 175lb, slim, 28 year old. I was recently diagnosed with type 2 diabetes, but I am questioning the possibility that I might have Latent Autoimmune Diabetes. I have a fairly significant family history of type 2, but I do not fit the body structure or age of these family members. I did a recent A1C and C-Peptide at diagnosis. The A1C was 8.2. My C-Peptide was 0.8. My cholesterol is normal, blood pressure is normal, etc. I have been maintaining my sugars between 100-130 since I changed my diet and exercise routines about 1 month ago. I have also been taking 1000mg glucophage daily. I am a respiratory therapist, and I know how crucial it is to gain control over diabetes before it gains control over you. Can you give me some insight on Latent Autoimmune Diabetes, and let me know if you think it is a possibility that I may have it? Thank you very much!