Is proudness a synonym for contrition?
No. Contrition means being sorry for having done something wrong or having failed to do something right.
The word "contrition" means sincere and complete remorse. This word is seen earliest in the bible. Theologians use contrition to describe interior repentance. It's origins come from the bible and there are some more explicit definitions by the Council of Trent. The Roman Catholic religion has information dating back into the 100s b.c. regarding contrition.