BB is 38/18/2.5

I have $250
Villain has $280

I really struggle to play JJ against reraises. Is preflop and flop fine?

Party Poker
No Limit Holdem Ring game
Blinds: $1/$2
6 players
Converter

Pre-flop: (6 players) Hero is UTG+1 with J J
UTG folds, Hero raises to $7, 3 folds, BB raises to $24, Hero calls.

Flop: 5 Q 6 ($49, 2 players)
BB bets $38, Hero calls.

Turn: A ($125, 2 players)
BB is all-in $227.9, Hero folds.
Uncalled bets: $227.9 returned to BB.

Results:
Final pot: $125