25NL: shoving top two on drawy flop vs weak players?

[Maunzekater]

BB has rock tendencies (14/9/2.2/1000). His bet sizing is awful, weak=weak, strong=strong. It seems that he doesn't know what to do after the flop, when he's oop - especially at this crazy table.
UTG is a habitual bluffer and very loose preflop (65/15/2.3/185). Makes incredible bad plays like investing half of his stack with air on a three barrel bluff.
Notes say: slowplays flopped 2pair on 2suited board, bets strong when possible flush comes. Insane bluffer. Let him hang himself.

I call preflop b/c T8s has nice potential against the two guys.

Party Poker, $0.10/$0.25 NL Hold'em Cash Game, 5 Players
LeggoPoker Hand History Converter

Hero (BTN): $24.65
SB: $35.61
BB: $26.19
UTG: $35.04
CO: $25.66

Pre-Flop: T[img]/images/graemlins/spade.gif[/img] 8[img]/images/graemlins/spade.gif[/img] dealt to Hero (BTN)
UTG calls $0.25, CO calls $0.25, Hero calls $0.25, SB calls $0.15, <font color="red">BB raises to $1.75</font>, UTG calls $1.50, CO folds, Hero calls $1.50, SB folds

Flop: ($5.75) 8[img]/images/graemlins/club.gif[/img] 6[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/club.gif[/img] (3 Players)
<font color="red">BB bets $3</font>, <font color="red">UTG raises to $6</font>, <font color="red">Hero raises to $22.90 and is All-In</font>, 2 folds

I thought what i usually think in this situation, ahead of their range, protection, betting for value, blah blah. So i pushed.

However, i had the strange feeling that shoving here is wrong. I can't explain it, it's just a feeling, maybe similiar to what i feel in situation where i don't know any other option but to shove (and then regret it most of the time).

Quick check for sanity please.