Yes, DM can affect periods but only if blood glucose is very poorly controlled (in persons with marked weight loss or weight gain). Other situations are related to other hormone problems such patients with Polycystic disease can have DM and menstrual irregularities.
DM per say does not cause minute to minute mood changes directly but if someone has marked fluctuations in blood glucose levels specially frequent hypoglycaemia then mood changes can occur. In your case it does not seem to be related to DM.