I screwed up. Can I redeem myself?

I just started dating this guy and I really like him (I really like him and I know he likes me the same, possibly more). We were hanging out and he had "You should just go home" sarcastically and I thought he was talking to someone else but he was talking to me. So me, being spiteful, I got up and gathered my things and left. I turned around and came back but then he acted as if he didn't even care so I left again and went home this time. I didn't hear from him for the rest of the day so I sent him a text saying I was sorry and didn't mean to leave abruptly and I hope everything is okay. He said "I'm sleeping. TTYL." So I left it at that. The next day I got a text that seemed cold. I have apologized over and over and told him how much I like him. So he invited me to go watch football with him but I'm not even sure I should go. What should I do? Should I go or just give him some space?