Honestly i feel your first mistake was playing alistar with a Ezreal.
I try to stick with this rule
-Do I have a adc who gets bullied Easily?
If yes
-Play something with good harrass who can help push waves
-Do I have a adc who can fend for themselves?
I
If yes
-Play something that will be good for the team phase
Basically if you play two people who get bullied easily for they both lack wave clear, than you basically shot yourself in the foot. Good lane bullies like lucian and graves leave support mains open for creativity in what they get to pick. However if you have a adc who chose something that easily gets bullied like a Ezreal or a vayne, something that has to scale. Than you need to view yourself as a baby sitter, play something that can protect and is damn good at it.
Thresh, morgana, Janna, stuff like that
To answer your question though
What you are suppose to do is help the adc push the wave, for if you let the wave push to your tower the following will happen
-Your adc will miss farm for very few people are good at farming under tower, even in high elo
-You are both at risk for a tower dive depending on who you are against
-Your tower will now be slowly be chipped away piece by piece by the minions and the laners
You obviously do not want to let any of these three things happen. So push the wave back to the middle and beg for a gank from the jungler.