Can taking psychiatry medication lead to premature aging?

Nope: There's no evidence that psychotropic drugs have any positive or negative effects on ageing. What one does have to look out for however, is the potential for many of these drugs to cause weight gain. That in and of itself could make you feel old before your time.

No: No, actually psych meds have been shown to both protect and heal brain damage related to stress and aging. Ssris increase hippocampal volume, thereby healing harmful neuronal damage to this critical memory region of the brain. Lithium is neuroprotective(prevents age related brain neuronal damage)and at the 2013 apa mtg was shown to significantly reduce the risk of dementia in patients with bipolar.