Should the patient just go home with the diagnosis of a "sprain"?
No. The pronator quadratus fat pad is elevated, this is indicative of an occult fracture.
What would your next recommendation be?
The patient can be immobilised and return for repeat x-rays in 7-10 days or the patient can have CT. Both are reasonable options and depends on patient preference and availability.
The pronator fat pad is elevated and there is soft tissue swelling over the dorsal aspect of the carpus. There is strong suspicion for a distal radius fracture but one is not identified.