I have a 2003 F150 4x4 7700 model the trans is slipping it feels like in second and when it shifts into 3 rd it’s with a god aweful bag I don’t know which auto tranny I have because the info isn’t on the inside door Jam or door

 

It's most likely a 4R70W. It's rare, but it might have a 4R100.

Crawl underneath and look at the transmission pan. 4R70W is rectangular, 14 bolts. 4R100 is shaped like Utah, 20 bolts.