Hair loss is frequently linked with topiramate. If a drug has the potential to cause hair loss, it means that it can cause the pathologies that lead to it including making your hair brittle and coarser. Some may experience hair loss while others may only go through the changes leading to it.
As for the skin, sodium channel blockers can affect the synthesis of collagen type I and type IV related to vascular structures and skin. Additionally, topiramate dehydrates the body and it is possible that the effects you are seeing on your skin are a result of it.