Asked a guy (that I have to see one last time) out and he never followed back up. Now what?

I have a class with him and he is a little bit older.
I thought for sure he was interested, but shy.
ie: switching seats to sit right across from me halfway through semester.
Speaking to me but hardly any others in class.
Laughing at my dumb jokes.
Catching him staring and looking away.
Seemingly trying to impress me with stories.
Basically finding any way to talk to me.
I could go on. But everything is subtle enough that he could just be very friendly or just interested in me in a platonic way.
At first I was disinterested, but I began to become more into him.
I decided to make a move and ask him if he wanted to hang out.
He initially said something like "are you sure you want to hang out with me?" He went on to say yes we can try to hang out but he is a pretty busy person. He then said he would message me. He said it was awesome that I asked him out and then said thank you.
I felt that it didn't go great with his vague answer and it seems guys say use "I'm busy" to avoid women they aren't into.

But minutes later when I got home I saw he had already emailed me saying that I caught him off guard and asked when we could meet up for drinks. I told him my availability and I haven't heard back since. (Just under a week now).
Anyway I have to see him in class real soon and I am dreading the awkwardness. I never asked a guy out before and I don't handle rejection great.
I am wanting to just skip class but my friends are talking me out of doing that because it looks like I am afraid/avoiding (which I am).
Just looking for some advice or thoughts on how to deal with this and the confusing behavior?
Thanks!
Asked a guy (that I have to see one last time) out and he never followed back up. Now what?
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