I flopped a set of Jacks on the flop. How should I proceed on the turn?

Was my Pre and Flop play ok?

Winning Poker Network (Yatahay) - $0.10 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4

BTN: 116.2 BB (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 1)
Hero (SB): 100 BB
BB: 107.3 BB (VPIP: 18.03, PFR: 15.70, 3Bet Preflop: 6.67, Hands: 122)
UTG: 62.2 BB (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: -, Hands: 1)
MP: 89.6 BB (VPIP: 100.00, PFR: 100.00, 3Bet Preflop: -, Hands: 1)
CO: 109.9 BB (VPIP: 0.00, PFR: 0.00, 3Bet Preflop: 0.00, Hands: 1)

Hero posts SB 0.5 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.5 BB) Hero has J J

fold, MP raises to 3.5 BB, CO calls 3.5 BB, fold, Hero calls 3 BB, fold

Flop: (11.5 BB, 3 players) 5 J 4
Hero checks, MP bets 11 BB, CO calls 11 BB, Hero raises to 35 BB, MP calls 24 BB, CO calls 24 BB

Turn: (116.5 BB, 3 players) T

I would squeeze pre.
Unfortunate turn card. The next bet has to be a shove and I doubt worse hands are going to call often. MP looks like he might be fish who could call JT but you block that. This is a x/f to a shove. Idk what to do if they pick a smaller bet size.

Just realized you're holding Js. Not sure how much that changes your equity vs their shoving range but it definitely improves it since they can have weaker flushes.

Raise pre, your OOP multi-way with a premium hand

As said above, I'd squeeze pre too.

Just GII OTT, it's a nasty spot, but given stack sizes we'll have to call a shove with Js here and there's definitely villains who can't let go of overpairs w Xs/pair + As here who may call, and some sets that people can call thinking they're getting about the right odds.

SQUEEZE ^

I don't mind the flat preflop. If you were on the BTN I squeeze here almost always because you have position which makes the hand infinitely more easy to play when called. When you squeeze from the SB and get called you're going to get put into enough tricky spots with overcards so I'm good with the flat. As you move up in limits and/or get more comfortable with your post flop play you can mix in more squeezes with JJ OOP.

As played shoving is your only option on the turn with a half pot sized bet left. If you were super deep checking would be an avenue to consider but not here.

EDIT: Best case scenario all-three of you get all-in. I think you're ahead of MP unless they have overs with suited spades but overpairs are heavily in his range. CO is the most likely to be on a a draw. I like shoving over check calling because MP is more likely to call your shove when behind if you bet, he calls and CO calls. If you check, MP checks and CO shoves then MP will likely fold hands you're beating when you call and he has a clear fold.

squeeze pre is fine, but calling is not bad at all.

Turn should be an easy gii.

3-bet PF. I think our hand is a little too strong to call against a MP raise and CO cold-caller. Against an UTG raise and MP cold-caller, I think it's a little closer.

Shove turn IMO. We've only got 61.5 BB on the turn, so we're forced to c/c for stacks if we check (we have at a minimum 10 outs if behind + we're ahead a small amount of the time + spades are okay a very small amount of the time if behind), and so we should bet instead. We get some value out of, I dunno, overpairs with spades, AsJx, and sets. Maybe something like QsQx folds sometimes. It's not a lot, but it feels better than the alternative.