You can, but it may be hard to figure out exactly what's happening without experimenting a bit.
Botox and Dysport are similar products but they're not exactly the same and so, at least in theory, you could have a "reaction" to one but not the other. But there are many other factors that could play into it, such as how strong a dose you got from each of them. That's normally counted in the number of units, and it's about 2 or 2.5 units of Dysport per unit of Botox. So you may have had a larger dose with one than the other.
You should discuss these issues with your physician and then it may be appropriate to go back to whichever of these products you prefer. It might be interesting to see if you have the same reaction to Dysport a second time...but you may not be in the mood for experimenting...
At any rate, go over all of this with your physician, and you'll be able to figure out a course you'll be happy with.
I hope that this helps, and good luck,