There are many domains registered like promptcare.com, promptcaremd.com etc... but "prompt care" as a phrase is a thing. promptcare.com 1,220 USD 2016-02-18
There is a chance someone might be interested in PromptClinic.com, but I guess it's an awkward phrase with only ~400 search results for "prompt clinic", compared to ~180,000 for "prompt care". So I'd say maybe $100-500, maybe nothing.