Questions: Flirting

I'm in university and there's this guy in my class who I think is super cute but he seems to be more on the awkward or quiet side? Like in a group setting he's definitely more likely to stay on the side and maybe throw out a witty remark but definitely not one of the people who are the center of attention. He's relatively quiet most of the time but obviously more comfortable with people he seems to be better friends with.

I haven't really gotten to talk to him much but usually when we have he's still pretty quiet. Like he'll make some stupid joke occasionally but still relatively quiet. Something I noticed though is that this boy hardlyyy ever gives me any eye contact. He'll stare off at whatever in front of him while we're talking. But while he's walking with another dude or even a girl he's kinda friends with he can look at them just fine. Like if I'm sitting next to my friend he'll look at my friend at talk to them ok but he won't look at me.

The thing is I'm an awkward girl too. Really shy and awkward and can't really find the right words to say. So I can't tell if it's just me making things uncomfortable in general. When we text though (we've only had like a solid 3 convos through text which I initiated) he's really fun and talkative. I felt like it was so natural and fun which doesn't just happen with anyone for me. None of that comes through in real life but I think thats just the awkwardness. I really want to get to know him more but I don't know if I have a shot because he never initiates convo.

Also one time I sent him this dumb Instagram reel that was like "the person with this initial owes you ______". and he responded with something like "maybe sometime but my schedule has been all over the place". Was that just him trying to let me down nicely or is he actually down to hang out? I wanna keep trying to text him but I don't want to bug him if he's busy or just finds me uncomfortable.

If anyone has any advice that would be so great. thanks!