Hi it sounds like you depressor anguli oris muscle was inadvertently treated on one side. This should be easy to fix by treating the other side. You should have someone who is experienced in treating this muscle fix the problem.
Sorry to hear about your experience. The Botox probably diffused to one of the lip depressor muscles. While it may take 3-4 months for your smile to return to normal you could see improvement in as short as 4-6 weeks. This will resolve as the Botox wears off. No permanent damage has been done.