Green’s Dictionary of Slang

(US campus) someone who acts as if they are better than others; thus pomp up, v., to give someone false praise.

1937		Z.N. Hurston Their Eyes Were Watching God (1998) 133: It was generally assumed that she thought herself too good to work like the rest of the women and that Tea Cake ‘pomped her up tuh dat’.
1948		Z.N. Hurston Seraph on the Suwanee (1995) 916: Who’s been pomping you up so? Who’s been telling you that you’re pretty?
1996		Eble Sl. and Sociability 64: ‘Someone who acts as if he or she is better than others’ was a pomp, a clipping of pompous.