Singles And Dating Open Question Should I Give Him Space Or

so basically, there is this guy who is in a couple of my classes. he thought i was cute and he asked my friend about me. he then gave me his number through Instagram and we texted a connected instantly. We hung out during lunch and after school. He opened up to me and we had a deep conversation. He would tell me how amazing i am. He told me that he is starting to like me a lot And he also took the time to meet my mom.
But the thing is, every time i bring up his name everyone either says he is a flirt or a lot of girls like him. And that made me suspect things. I started to over think everything and i felt that he was using me. But it was just weird for me because he knows so many pretty girls and out of all of them, he chooses me. He also hangs out with a lot of girls too. But i guess that's just who he is because he hasn't really had a father figure growing up.
So a couple of times i asked him, do you flirt with a lot of girls and he said no. But it didn't seem sincere. And then i just got tired of everyone telling me those things about him so i decided to just believe everyone else.
So in class the other day, he asked if i was mad at him and i just ignored him. and then next class i had with him he was ignoring me. I asked for a piece of paper and he didn't even answer me and that kind of bothered me. So i passed him a note saying "if you're mad at me, you shouldn't be. i didn't do anything wrong" and he passed it back saying "you're mad at me, remember?" and i said "well i have a reason to be, i'm hearing all this stuff about you and i don't know what to believe...i'm starting to think you're just using me." and then he reads it and just crumbles the paper up. He doesn't even respond. And that made me sad.
So i started to feel bad because i kept bothering him with the whole flirting thing. And i regret it so much. And of course after i ask him about the flirting thing, i hear that he actually does care for me and like me. And i heard that he told this girl not to touch him because he doesn't want me to think that he likes her.
I just feel so bad for everything. I shouldn't have believed what people were saying. So today i try and talk to him again, but he ignores me. I already apologized to him and i admitted to my mistakes through text and he never responded.
Should i give him some space and give him time to think? Will he come back? How should i act around him? I'm sad but should i pretend to be happy? I just need some advice please.

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