You'd be a douche if you were only biding your time with Rebekah, just so that, when you got the green light from Christine, you'd be able to drop Rebekah without caring about her any further. You'd also be a douche if you where showing interest in Christine while you were still with Rebekah. In either case, the decent thing to do in either scenario, would have been to end things with Rebekah first before showing interest in someone else, so that, both of you had a chance to come to terms with the end of the relationship, or rather, in this case, she had a chance to come to terms with it, and then moved on.
If you did either of these, then yes, you'd be a douche, well, not so much a douche, rather than an asshole really, for the way you handled things at the end of your previous relationship, as opposed to how quickly you rebounded from it. I'd like to say that this sort of thing is limited to teeny-boppers in "high school" relationships, but it isn't.. there are adult assholes who do this as well, even worse, when they are in more serious relationships than that you'd find in high school.
While it is just as wrong, and the adult who did this is still just as much an asshole, as a teen who did the same, it is WORSE because this is selfish, and immature behavior is ALMOST ALWAYS expected of teens in "high school relationships" and not an adult as we are supposed to have graduated, mentally as well as physically from high school.. as we are supposed to have grown past it. As adults, we are not supposed to be the same person, we were in high school. We are supposed to have grown up, and have our priorities in order. We know that we are to be responsible for our actions, and know that we are supposed to conduct ourselves as responsible individuals. Teens in general, are regarded as immature, reckless, selfish, flaky and irresponsible people, and in high school, they will meet and "fall in love" with the "love of their life" about a hundred times before they even graduate.. and they will then go on to lose interest in that same person a few days later, or when things start to get hard and start the cycle up again with someone new.
This is why these "relationships" rarely last outside of high school, and in the harsh light of reality. The ones that do, do so, because both people were mature enough to realize that the relationship may not last, and gave themselves time to grow up and apart and go separate ways, and then got back together much later on in their lives just to see if there was something there.. sometimes there is, but most times, there isn't. Furthermore, this is why most parents would roll their eyes and take these "relationships" with a grain of salt. So, depending on which scenario applied to you, you'd either be a douche or an asshole, or an immature and selfish douche or asshole, but if you are still young, then it isn't so bad, as this sort of behavior is expected of you.. and being young, you can still grow up to be a mature adult.
You would only have reason to worry if you were say, my age, and doing this sort of thing, as you are supposed to know better. You'd still be a douche for the way you handled things toward the end of your relationship with Rebekah, because whether you are 16, or 28, there is still a right, and a wrong way to do things, but hopefully you will learn from this and will know in the future to do the right thing from now on.
People are different, and so, there is no set amount of time for how quickly a person is supposed to rebound from a relationship. If you cared about the person you were with, and had been through a lot together, and were together for a long time, then of course, it stands to reason that you would take a while to come to terms with the end of your relationship, and you'd take even longer to rebound from it. Most would quickly seek to be with someone new immediately after and often times, these relationships will fail as it is obvious that it is a rebound relationship. Once that person becomes aware of the situation, then they won't want much to do with you, unless, their self-esteem and self-worth is in the toilet. In that case, you have much bigger problems to worry about.