Thanks for the query. These are possibly comedones and removing them with nails may cause a problem, you need to find why are they happening and it can be done easily by consulting a dermatologist. Salicylic acid based face washes can work well for you and chemical peels in multiple sessions can also be considered. Kindly consult a dermatologist for precise treatment plan
Next Steps
You should definitely consider your treatment under the guidance of an expert qualified dermatologist
Health Tips
You can consult me online for personal recommendations