Nose is very sensitive because many nerves are there.

Nerves are the little things in your body that tells your brain “phew, thats hot” or “ouch, that hurts”. More nerves - more hurt. And many nerves are in/on/around the nose.

Try to rip out a hair from your head. See how much it hurts.

Then try to rip out one of the tiny (or, if you are older, not-so-tiny) hairs inside your nose. See how it hurts compared to the head hair.

Head has not so many nerves around where you rip the hair out. Nose has plenty of nerves where you rip the hair out.

Thats why pimples are so painful on the nose.