Is it normal to feel guilty for moving on?

Okay so I "dated" this guy off and on for over a year. I say "dated" because it was a long distance thing, so I only saw him once over the whole course of our relationship.
It was a very unhealthy relationship but I still stayed with him. He broke up with me twice for different girls in his town and I looked past it both times. I couldn't even count the amount of times we broke up and I was often very unhappy with him.
Anyway, about 3 months ago, I broke up with him for good and I've now moved on. He still tries to talk to me over Facebook or text message sometimes, but I just can't handle it.
Today my crush whose been flirting with for a few weeks asked me to be his girlfriend, and
of course, I said yes. We spent the whole day together (yes, hooking up often) and it was an amazing time. But now I'm sitting at home thinking about my day, and I find myself feeling horribly guilty.. My ex and I are clearly broken up, and I have NO feelings for him whatsoever, but I feel horrible for having so much fin with this guy, while my ex and I never had the opportunity.

Is this normal?