flopped FD + pair

Ladies and gentlemen, what is your opinion on this hand? Villains often re-raise with top pair or FD on flop. He rarely has overpair (would have 3bet me PF) or set (JJ is 3bet, I block 9). On turn le wild 7 appears in and I suppose he does not have 7 and I shove my FD with pair on turn. Sure I am lucky in the end, but how about him - It is fold right? I have a lot of fold equity, just don´t expect here to be called with AJ . Zoom poker, no history on that guy, he hasn´t history or read on me (99,9% sure).

Question is: Is my play in this hand profitable in long term? Should I have shoved already flop instead of raising? THX.

Hand History driven straight to this forum with DriveHUD 2 Poker Tracking Software

NL Holdem 0,10(BB)
BTN ($24,39)
SB ($12,13)
BB ($10)
UTG ($10)
HERO ($10,31)
CO ($12,96)

Dealt to Hero: A♠ 9♠

UTG Folds, HERO Raises To $0,25, CO Folds, BTN Calls $0,25, SB Folds, BB Folds

Hero SPR on Flop: [15,48 effective]
Flop ($0,65): J♠ 7♠ 9♦
HERO Bets $0,24 (Rem. Stack: $9,82), BTN Raises To $0,79 (Rem. Stack: $23,35), HERO Raises To $2 (Rem. Stack: $8,06), BTN Calls $1,21 (Rem. Stack: $22,14)

Turn ($4,65): J♠ 7♠ 9♦ 7♥
HERO Bets $8,06 (allin), BTN Calls $8,06 (Rem. Stack: $14,08)

River ($20,77): J♠ 7♠ 9♦ 7♥ 9♥