I just broke up with a guy about 3 weeks ago, is it too soon to take interest in someone else?

That is completely up to you. If you end up liking them that soon there is nothing wrong with it and its nothing you can control. I personally like the same guy for about 2 years but before that I was all over the place trying to find the right person. You just have not found the right person yet. Hope you do soon though :)