The main problem was that his poke was doing more damage than mine, so he would win every trade and just dominated the lane.
Generally speaking - you don't want to try poking Teemo as anyone in top-lane.
You want to go ham on him until he's dead, and then teabag his corpse.
Teemo's all-in damage is incredibly bad.
His QWER burst rotation is Blinding Dart and nothing else, and his AA poison is significantly weakened when successively striking the same target, seeing as that mostly just resets the duration, with a small amount of up-front damage.
You pretty much have to let him place a mushroom under your feet and wait for it to detonate for that to go in his favor.
Inversely - Teemo's poke damage is very, very strong. He's got far beyond Kayle's AA steroid and manaless taboot if you let him trade 1 AA then back off, trade 1 AA then back off. He'll win doing that unless you simply out-range him to such an extent you can AA him and back off without even getting shot back, which most bottom-lane picks can pull off.
The general trick with Teemo is just staying far enough back he can't AA you - until he gets in a position where you can safely retaliate and unload everything. Then you retaliate and unload everything.
Works out extra-well if you manage to be within range of Dart and not his AA's, so he pokes with Dart right before that - leaving it on CD when you jump, and allowing your auto-attacks to add some extra DPS.
That's how I beat him with Vayne and Fiora at any rate. Had to learn some tricks when those are my favorite champions :(