I am afraid that you have ruined your rifle by using a bore brush on it. If you will pack it up and send to me, I'll dispose of it for you- no charge- 'cause I'm a nice guy.
Yes, I am only kidding. A new barrel may have some breaking-in to do- simply wearing machined parts smooth. A bronze brush cannot hurt a steel barrel. Yes, that was lead you saw.
Ref: washing your hands, soap and water. Hot or cold does not matter. If your brother says something about hot water "opening your pores and letting lead in" he must have pores the size of a softball- lead is not a skin penetrant hazard, unless it is moving at high speed. But washing hands after cleaning a gun, shooting, or handling ammo is a very good practice to follow that many folk miss. Lead is taken into the body by inhalation- breathing it, and by ingestion- eating it.