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.
Your dermatologist will decide a treatment plan for you after a consultation.
Apart from active pharmaceutical medicines, a healthy diet and lifestyle is mandatory to achieve results.