Neither of you need to convert each other, and if you're both (or just one of you is) adamant in your views, then trying to debate your reasoning might just cause more problems.
Instead, I would ask your mum to sit down with you quietly, and explain to her that you've come to your belief by yourself.
The school hasn't tried to convert you and they aren't trying to disrespect christian belief when they teach evolution.
Explain that you want to stay at the school.
And explain that you still respect her beliefs, and you want her to respect yours too. You don't want to argue over them, and you don't want them to get in the way of each other. You can still both get on and love eachother without having the same beliefs.
Then give her a cuddle.
