Let's see...
I can't really think of much problem vs Shen except if you let him poke you over and over with his Vorpal blade, you should be overly agressive with him to force him to pull back, without losing too much CS, of course.
Renekton is a bit of an asinine lane, since he is an early bully whereas you're not, unless you can find a good opening, I suggest to keep yourself alive and farm, you WILL outscale him, specially at lvl 9 with your main powerspike with W (unless you want to max E for the stun).
Vladimir is another bothersome lane, I find myself rushing BoRK instead of Trinity force a lot vs agaisnt this guy, this lane is one of the ones where I prefer to get Q at lvl 1 instead of E so I can last hit minions without letting him punish me too much, that's the key component here, don't let him punish you too much, specially when he begins getting enough HP to charge his AoE spell (I think it was E?).
Many of these require you to keep yourself alive and farm up, since Irelia is extremely item reliant.