The first motel to use that name in the US was built in California in 1925. Motel - Wikipedia
This site gives links to various Montgomery County (or Montgomery Co related) organizations including the Silver Spring Historical Society. Preservation and History Organizations - Montgomery Preservation
The earliest city directory for Silver Spring that I could find on-line was for 1958 (a bit later than the years you listed) and there were only 2 motels listed: Highland Motor Hotel (8134 Wisconsin Ave, Bethesda) and The In Town Motor Hotel (8000 13th St, Silver Spring). There is a postcard of the In Town Motor Hotel In Town-Motor Hotel Silver Spring, MD Postcard (cardcow.com).