It is not dangerous in and of itself to pick at your fingernails rather than trimming them with clippers. The main reason why people avoid doing this is cosmetic - picking at the fingernails does tend to leave them a bit more jagged than if you trim them carefully with a nail clipper. Therefore, if the cosmetic appearance of your nails is important to you, using a nail clipper might be helpful.
Furthermore, you have less control when picking at your nails than when you use a nail clipper. Therefore, the risk of accidentally peeling back to much of the nail, potentially causing damage or irritation to the sensitive skin n the nail bed, is higher. If you find that you ever do accidentally peel back the nail too much, make sure to leave the damaged nail in place - further attempts to peel the nail back before it grows in will just lead to more pain and potentially put you at risk of infection of the area. Instead, cover the area with antimicrobial ointment and a bandage until the nail grows back and the discomfort is grown.
I recommend checking in with your primary care doctor
about this soon. This sort of general health question is perfect for that setting.