Some medications can cause severe skin reactions and conditions. This is mostly a side effect of the medicine. Generally, most medicine are not harmful to the skin because not all medicine act on the skin.
People who often take Saint John's wort( herbal supplements works as antidepressants), aspirin and other non steroidal anti-inflammatory drug are likely to have bruises because these drugs are blood thinners, a little accident can cause bruises. Lithium, a medicine use to treat epilepsy and bipolar conditions is known to aggravate psoriasis, it can also cause severe acne and folliculitis.
In summary, it all depends on the medicine you are taking and how long you take a medicine before side effects like skin reactions become visible on your skin.