This was by the Arizona Cardinals vs Green Bay Packers on January 10,2010 when Arizona scored 51 points and Green Bay scored 45 points which came to a total of 96 points. Which makes Green Bay the highest scored losing team with the most points in the NFL history.
the most points scored is 186 by the Detroit pistons
Wyoming scored 103
The Detroit Pistons scored the most points in a great game at the Denver Nuggets.
In the NFL, 29 has been scored: 22 times by a winning team 14 times by a losing team.
If you mean in one game, in Super Bowl 24 the 49ers scored 55 to the Broncos 10 for the most points scored by one team in the Super Bowl.