TT in SB facing UTG open from relative unknown

I feel like I played this hand quite badly (which is why I'm posting it) but I have no idea what I could do better, so I'm really interested to hear analysis at every point in the hand.

UTG is 22/19 over a very small sample (30 hands) so likely to be standard TAG probably. I know absolutely nothing about BB.

I 3bet pre because I feel like my hand is too strong to just fold, but too weak to call OOP.

OTF, I feel like not only can UTG stab because of position, but also after the preflop action, he can't feel super comfortable being checkraised here if he holds AQ/AJ, I think we can discount AA/KK because he's unlikely to want it going 3way once the SB calls preflop.

As far as plans for future streets go, if I get raised on the flop I'm obv folding, and if I get called on the flop, I'm planning on shoving any non A/Q/J turn and giving up on an A, Q or J.

Poker Stars, $0.10/$0.25 No Limit Hold'em Cash, 6 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite.

BTN: $34.11 (136.4 bb)
Hero (SB): $33.70 (134.8 bb)
BB: $28.39 (113.6 bb)
UTG: $70.40 (281.6 bb)
MP: $25.35 (101.4 bb)
CO: $12.85 (51.4 bb)

Preflop: Hero is SB with T T
UTG raises to $0.75, 3 folds, Hero raises to $2.25, BB calls $2, UTG calls $1.50

Flop: ($6.75) J 2 Q (3 players)
Hero checks, BB checks, UTG bets $3.50, Hero raises to $9.75,