Why didn't Jesse kill Walt? Would he have done it if he hadn't of realised Walt had been shot.
Because he realized it was pointless, and because he also didn't want to do what Walter told him to do any more.
Jesse finally walked away and made his own conscious decision to let things go, and not follow down the downward spiral any more.
Walter could always have done things himself. It's what he did this entire episode, and that's why Jesse figured he might as well do it himself.
Watch the scene in the jail, the police tell Jesse the doctors believe it's ricin because Broke is responding to their treatment. This very very clearly implies that they believe ricin can be treated.
It's because he was responding to general treatment for poison, and they knew he had been poisoned; not necessarily that it was ricin. They assumed it was because they got the hint, which came out of the blue.
Ricin is a potent and rare type of poison. For him to completely come out of nowhere and suggest that it was used is clear cause for investigation. It gave credence to the notion that he was poisoned (and Brock did show flu-like symptoms supposedly which was another connection), but that it was ricin was just a suspicion.