Can psychiatric medication damage your brain over time?

Yes they can: Well it depends on various factors including, what medications, what dosage, length of their use and stage of life they are used in and this last factor is the most important piece in this puzzle. Human brains go through the process of brain development specially during the early years and psychiatric medication use during that time might have long term sequelae on brain development.

Psych MEds: Psych meds if used correctly are neuroprotective, older generation antipsychotics may permanent tremors and parkinsonian like features in patients on long term treatment, newer generation can but risk is low.

Brain changes: The intent of prescribing psychiatric medications is to affect the brain improving its function and performance. It is beneficial to produce long term effects on a diseased brain, and to reverse the mechanisms of disease if possible. Most of current treatments produce those changes only if administered every day, and the effects last shortly after discontinuation. One exception is psychotherapy.