According to the description of a “purple nail sensitive to pressure” after trimming it, you could be experiencing some type of nail infection, or "panaritium". Nail infections can occur after cutting the nail and damaging the surrounding tissue. Simple panaritium can be treated with local antibiotics. Sometimes panaritium can be due to nail growth into the surrounding tissue (unguis incarnatus). Unguis incarnates is treated surgically by removing the nail. These types of infections can be prevented if nails are not cut very deeply.