Thornmail is pretty low as far as health goes (just 100 more than a health crystal), Frozen Heart has 0 health, and Sion actually has really low base health (the W passive makes up for it). Frozen Heart and Randuin's Omen also don't get to affect Yi with their passives because of his ult. You pretty much went straight into the worst items against Yi you could, at least if he isn't going crit which he probably isn't.
I would recommend getting something like a Sterak's instead of Thornmail (which you don't want to stack with Randuin's anyway, unique passives and such) and something with health rather than the Frozen Heart, even if it is an MR item. Sion is also one of the worst champions to deal with Yi on since you will never cc him outside of the occasional point-blank R, but you can't always avoid the match up.
As for killing squishies, Yi probably does it in closer to a second if you don't include the time for Alpha Strike. However, if you keep track of where he will come out of Alpha, even Sion can land cc.