Sweeper Sweeper Sweepers
To be honest, beating AP Teemo requires smartness. I played him since Dominion came out, so i will say a few tips
Sweeper is good for bushes and speed shrine and health packs on their side of the map. Don't blindly use them everywhere because it has a cooldown. This is not the case if you keep loosing your mid and bot, because the more map control their team has, the more area Teemo can safely and repeatedly shroom
Watch where Teemo goes on mini map, if he never got as far as your mid, you don't have to worry about that health pack near your mid at all.
Learn his pattern, every Teemo is different, but there are big bushes. If he shrooms the right side of the bush 5/6 times, then you can enter the middle and the left.
If he shrooms the top half of a speed shrine (auto path takes you there), then you manually control and go thru middle. Learn it, remember it, and avoid it.
Play a bit more differently, don't just hide in bush and come out hoping its easy to destroy them, because chances are their shroom will hit like 4 people. Be careful, don't all stick together next to each other. when you are on the move.
Also champs like lux or morde is great, because it can scout bushes with its shield, and bam, deals very low damage.
And it is wise to eat a shroom on purpose, especially you can take 2 ticks of damage and you are about to recall. Clear it with your body if you can take the pain and will be safe (such as when their team is on respawn timer)