You may want to check out the following site
http://www.vrbo.com/
You can do a search of Myrtle Beach and they have some pet friendly houses/condos listed. You may also want to check out Lands End condos, they noted some of their units are pet friendly. We are going down next month and it hasn't been easy finding pet friendly accomodations.
Dogs are not allowed on the beach from 21st Ave N to 13th Ave S period. You can have them on the beach before 9 or after 5 but just not in the above area.