Yesterday, I asked one of my students how he was. He answered, "I am more better." I told him that "I am (much) better" would do. He answered, I was already better yesterday, and I am better than I was yesterday." It made me think twice. Was I wrong with my correction?
No, you aren't wrong.
The simple rule is this that you use 'much' ( instead of very, more etc ) with 2nd degree of adjective.
What your student should have said was this,
I am feeling better than yesterday
I am feeling much better than yesterday