• I recommended her that we should enroll in AT LEAST one class together. My reasons being is that I'll like to be the one who pulls her chair everyday or that I could have my girlfriend as my partner to do projects together.

As someone who had the same major as their high school sweetheart...don't do that. Choose whatever classes are best for YOU, and don't plan around your SO's schedule at this stage. Also make sure you do projects with all kinds of different people to network and socialise.

I was kind of hurt because my plans to appropriately flirt with her were shot down.

You have plenty of opportunity to flirt outside school