Small papule that is skin coloured on the side of nose grows back when scratched and bleeds. what could this be? skin cancer?

Yes but rare @17: I have seen bcc in a 5 year old but that is rare and he had a syndrome. It isoprene likely an inflmatory lesion or benign growth but see a dermatologist for a definitive diagnosis and possible biopsy or excision.

Nose lesion: This could a skin tag, pyogenic granuloma, or possibly a basal cell cancer in a fair skinned individual. It should be checked by a physician.