I really am supposed to go broke

[SplawnDarts]

Not sure I follow. You made a very convincing argument your opponent held AA. If that was your reasoning at the table, then your conclusion has to be that you're WB and need to check/fold. Which is what you did.

There are lots of situations where people say you "ought" to go broke, but very frequently they're wrong. There's no benefit to going broke here - it's straight up -EV.

You should be thrilled this guy gave you two free shots to hit your 2-outer. By playing it right you turned a 92% chance you go broke into a 8% chance you bust him. That's f'n great, not cause for alarm.