The Amazon Elastic Search service will certainly help you do most of the heavy lifting and you won't have to maintain any of the underlying infrastructure. However, elastic search isn't trivial in nature. Typically, this will mean several days worth of work.

Over time and projects, I've over the years leveraged another solution called Algolia Search. Algolia is a fully managed, search as a service solution, which also has SDKs available for most common languages, will answer your fuzzy search requirements, and also cut down implementation and maintenance costs significantly. You should be able to get a solution up and running within a couple of minutes to an hour.