First and foremost, fix that leaky sink!With that done, you can move onto fixing the floor.
Unfortunately, there's no easy repair for damaged laminate. The reason is this: It's difficult to replace just one piece because laminate is installed on a locked-together basis Sometimes it's tongue and groove style, but more often the pieces snap together. With, let's say, hardwood, if one piece is rotted or damaged, you can chop that piece out with a saw, cut the end of the groove off, drop a new piece down from the top and overlap with the existing piece. But you can't do that with laminate floors because it's all one piece, and it floats.
So stop that leak, and let the moisture dry to avoid the risk of mold. Then replace the laminate floor in its entirety. Some laminate is more tolerant to moisture than others, so shop accordingly if you think there's any risk of leaks in in the future. Good luck!