Is the shy guy into me?

Hi reddit users. I know a guy who's at my school, we met like a year ago but we're not friends or anything, we just know each other. About 6 months ago, I was rejected by a girl who I was in love with and I moved on. Then, I noticed him staring at me. We kept making occasional eye contact for the remainder of the school year, and sometimes it was awkward, but we didn't really talk to each other. Now, we're in the next school year, and we are in 2 classes, unlike last year, where we only had 1 class together. This year, a lot changed between us. At first, our eye contact continued. But then it got a little more 'suspicious'. I know it sounds weird when I say all this, but it's how I experienced it. And by the way, this guy's pretty shy, at least, most of the time he's pretty silent when I'm around. I will call him Billy for now. So, one day, I'm in class sitting at a table with my friend Joe, Billy and Billy's friend Samuel. I know Joe a lot more than I know the other 2. So Joe and I get into a discussion about music, and I say that I like Phil Collins, which should'nt have been a surprise, since I post a lot of Phil Collins stuff on instagram and snapchat. Then, Samuel snaps at me and says 'who the f*ck is Phil Collins?'. Billy, on the other hand quickly asks 'yeah, who's Phil Collins?', in a more interested tone. The next week, I show Joe some Phil Collins music, and Billy comes to us and he says 'it's not that bad'. I know, it doesn't sound like much, but it doesn't end there. The frequent and unnecessary eye contact between Billy and me continues. Then, one day, we have a test and he's sitting in front of me and he starts turning his head around and I notice him trying to look at me through the corner of his eyes. I know it sounds like he's autistic, but it's hard to explain the moment. Anyway, more of this kind of shit happens and one day, Joe and I talk about what we'll be doing tomorrow: going to see a movie. Billy quickly asks, 'what's going on tomorrow?'. I tell him we're going to the cinema. Billy gets interested, but the topic quickly changes. That afternoon, I ask him if he wants to come along to the cinema. He quickly replies within a few minutes and immediately asks who's coming along, which cinema. I tell him and he asks what time. I tell him the time and he says he unfortunately can't come because of a soccer match. He wasn't lying, a friend who's on his team actually asked him about the match earlier that week. Billy kindly says 'I can't come then, sorry'. I say: 'oh that's a pity' He says: 'yes' I say: 'it would have been fun' He says: 'yes unfortunately' So we go to the movies without him, and I never hear him talking about it again. Time goes on. Then, we get our first exam week. This is where shit takes a slightly odd turn. So, I'm sitting at a table during break time, and this annoying guy called Kurt won't stop talking. I see Billy walking down the stairs, he walks by us and stands at the other side of the table, where Samuel is also sitting with his girlfriend. Then, one of Billy's other friends, Bryan, also comes towards our table and sits next to me and Kurt. Then, within a minute, Billy grabs a chair and for some reason, decides to sit next to Bryan. Kurt keeps on talking, Bryan leaves for the bathroom, then Kurt leaves as well, and it's just me and Billy. Then Billy smiles and says: 'that guy Kurt is crazy'. We both start laughing so unbelievably hard, his face turns red. It was so weird realising that I was sitting there laughing with him. We had never had a real conversation and somehow we just start laughing like normal friends when we finally have one. After that day, it got weirder. The eye contact seemed a little more intense. We haven't really talked since that moment where we couldn't stop laughing. But I remember that on the last day of the exam week, I was at the bike rack, and I looked back, and I caught him staring at me. Same old, same old. Now it's been a week since the exam week and the staring and overall awkwardness has increased to an all time high. This guy has been following me on insta for a year but he has never liked any of my posts. And guess what, a week after the laughing incident he suddenly decides to like my post (which I posted on the same day as he liked it, of course). Very odd. Please tell me what your opinion is on this, whether you think this guy could be into me and what I should do.