“Are topical sprays good for sprains?”

Not proven to make a difference. Won't harm you though, so if it helps you, go for it.

Yes, topical sprays are good short-term. There are some good ones out there. I am particularly cautious about sprains as many doctors think they are nothing to worry about. I am still the old school. RICE: Rest, ice, compression, and elevation. Sprays help ease the pain, but should not be used so you can do more as in the long run it takes time to heal 4-6 weeks, in some cases 8-12. Do not overdo activity.
Hope this helps.

A sprain is a stretching or tearing of ligaments — the tough bands of fibrous tissue that connect two bones together in your joints. Mild sprains can be treated at home. But the injuries that cause sprains can also cause serious injuries, such as fractures. Initial treatment includes protection, optimum loading, ice, compression and elevation. The OTC sprays will help numb the area like ice would, but a visit to your physical therapist may be necessary if symptoms continue to go on.

They can help assist with minor to moderate Grade 1 or 2 sprains in the early stages yes, however the more intense sprains such as a Grade 3 may require heavier medication or possibly surgical intervention depending on the type. Hopefully this helps however you may want to talk to your PCP, ortho, or pain management MDs for further assistance.