44 2nl floped fh anyway of not going all in?

I flop full house in position villain check calls till river then donks pot size bet
I have TT in villains range, but so many others hands more likely, on river shove I think it is TT but am I ever going to fold my fh?

iPoker - $0.02 NL - Holdem - 8 players
Hand converted by PokerTracker 4

SB: 71 BB (VPIP: 62.50, PFR: 50.00, 3Bet Preflop: 50.00, Hands: 8)
BB: 44 BB (VPIP: 16.67, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 6)
UTG: 124 BB (VPIP: 12.50, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 8)
UTG+1: 108.5 BB (VPIP: 14.29, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 15)
MP: 97 BB (VPIP: 31.25, PFR: 18.75, 3Bet Preflop: 0.00, Hands: 16)
MP+1: 215 BB (VPIP: 62.50, PFR: 12.50, 3Bet Preflop: 0.00, Hands: 8)
Hero (CO): 98.5 BB
BTN: 45 BB (VPIP: 12.50, PFR: 12.50, 3Bet Preflop: 0.00, Hands: 8)

SB posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has 4♠ 4♦

UTG raises to 4 BB, fold, MP calls 4 BB, MP+1 calls 4 BB, Hero calls 4 BB, fold, fold, fold

Flop: (17.5 BB, 4 players) 4♣ T♥ T♦
UTG checks, MP checks, MP+1 checks, Hero bets 11 BB, UTG calls 11 BB, fold, fold

Turn: (39.5 BB, 2 players) 8♥
UTG checks, Hero bets 27.5 BB, UTG calls 27.5 BB

River: (94.5 BB, 2 players) 9♠
UTG bets 81.5 BB, Hero calls 56 BB