Alistar feels useless

The only time I play Alistar is when I roll him in ARAM. I feel so useless with him. His cooldowns are so long. In team fights, I basically do a combo and then bitch slap somebody for 9 seconds because EVERYTHING is on cooldown. He moves so slow, so doing his combo is hard enough as it is; plus, getting picked off seems to be a really common thing. He basically is sitting in the dead champions bin right now.