Customs and immigration – Denied entry at the Canadian land border; Will I be denied if I fly?

I was recently denied entry to Canada, because I wanted to bring my other wheels for my vehicle to store at a U-Haul center until I started school in Canada in the spring.

They thought that, because I was bringing my wheels, I was trying to stay illegally until school starts. Also, I still do not have my study permit. They thought I would come and I would stay to get it when I started school.

My main reason to go was to spend the holidays with my girlfriend. I really want to spend the holidays with her. If I bought a plane ticket to Canada, would they have my refusal registered and would they also deny me at the airport?