Suicide: Yes (New York Times, study), but not just millennials:
> Suicide in the United States has surged to the highest levels in nearly 30 years, a federal data analysis has found, with increases in every age group except older adults. The rise was particularly steep for women. It was also substantial among middle-aged Americans...
Accidental Drug Overdoses: Again Yes (New York Times), if by "millennial" you mean "young whites":
> Drug overdoses are driving up the death rate of young white adults in the United States to levels not seen since the end of the AIDS epidemic more than two decades ago — a turn of fortune that stands in sharp contrast to falling death rates for young blacks, a New York Times analysis of death certificates has found.