Sonya,Three days is not a problem. In fact many times for the lighter peels, we do the two treatments at the same time. As noted by others here, the two services work beautifully together. You should not have any problems with the time frame you have mentioned.
There is really no reason why you could not proceed with a peel 3 days after Botox. The Botox may enhance the rejuvenative effects of the peel.