Poppy can be very good on solo top, though I prefer her bot lane with ad carry. Your problem is, that your passive only reduces nukes, champions like garen will destroy you with his dmg over time.
Poppy is an assasin and that's why you got owned by shen, you need to deal enough dmg that your enemy retreats, because if you don't, ex: I hit gp into wall, and q him, he runs away from me and creeps. is good. other ex: You hit Garen and q him, you deal dmg, but then he q's you and spins you to under halph health.
Poppy is generally good pick solo top, but mostly for counter, because there are more match-ups where she gets owned, than where she owns. Also depends alot on ad or ap