Is it possible to search for terms among ONLY the people I follow? I know twitter.com allows it, but does the API? If so, is there direction on how? I’ve searched up and down for this with no success.
No this is not an option in the Search API.
There’s an “awkward, but seems to work” way, if you add people you’re interested in to a list, and use that in the query, eg:
list:NASA/astronauts-in-space-now in the query will only return results from @NASA astronauts-in-space-now list https://dev.twitter.com/rest/public/search