Bf asked for time/space and when I see him in public he avoids me like the plague?

It's been a little over a week but the last thing he said was that he needed more time to see if he wants to be in a relationship after I expressed that something in the past he did to me hurt me. He got really upset and tried to blame me for it. He said he needed space/time.

But everytime I see him in public he avoids me like the plague and just leaves as quick as he can. But when I text him to see where he's at, he respectfully. Should I just leave him in his world of time/space and date this other guy who asked me out?

He used to avoid me like this when we were broken up the first time. So I'm like okay are we broken up or...?