I need to drive a 7/16" nut but am unsure how to use the socket I bought for my screwdriver
You need two things.... 1/4" drive 7/16" socket



...and a 1/4" hex shank socket adapter...



That adapter kit will allow you to use multiple drives of sockets for hundreds of future uses. You probably already have some sockets. There are some one piece cheapos on the market that do work, but you have to buy all new kits when either the shank or socket portion wears down or breaks.