He didn't poison himself, nor would he have. I think he was stressed, strained, and life weary after the Crimean War, as well as getting older, so it's natural he came down with an illness that led to death. I think his attitude may have been rather life weary, but I think that's the extent of it. His death was natural, whatever he was feeling, poisoning himself woudn't have occured to him.
Agree with you, I don't believe that he poisoned himself, from what I read his health began to deteriorate some time before his death (as well as the health of Empress Alexandra), and also he was completely demoralized by the tragic news that came from the war in Crimea, if I recall correctly Sevastopol was under siege, and the situation was desperate.
According to historian Henri Troyat, the Tsar stopped to take care about his health, but his death was natural.