There could be three reasons you still see the same wrinkles present two days after your first Botox injection. First, Botox does take several days to achieve maximal muscle-weakening effect, as the other answers state. But more importantly, many patients have unrealistic expectations about what Botox can do right away, or at all. It's very important to understand that Botox only weakens muscles under the skin. It does not have any immediate direct smoothing effect on the top of the skin. This means that if your lines are very deep, from many years of making the same expressions, at first the Botox or Dysport may only stop you from making the expression, and folding the skin there, as deeply. You can imagine that it would take a long time, weeks to months, to maybe even years, for deep creases to smooth on their own after the muscles don't fold the skin anymore. This is why it's important to make a bit of a commitment to trying these treatments repeatedy (every three months or so) for at least a few cycles, so you can eventually see the cumulative effect of the long term relaxation. Bear in mind that the popular online myth about anything ending up worse off if you start and then one day stop is just that, a total myth.
Finally, a third reason your wrinkles are still there, is that sometimes doctors try to use Botox to do more than it can really do. If you have a lot of excess skin and deep folds, not just lines, it may be that you do need surgery to lift or tighten the area, and that Botox weakening the muscles under there just can't do enough to make a difference. This is why it's so important to go to a legitimate, honest, trained physician who can properly identify this situation, so you don't waste months and money when Botox or Dysport can't really do the full trick, and they can guide you in a more useful direction.