When researching Asian history there are a number of geographic subject terms you can use:
This subject heading is broad, and covers the entire continent.
Includes resources related to China, Japan, North Korea, South Korea, and Taiwan.
Represents works dealing collectively with the mainland and insular regions of Asia (south of China and east of India), including Burma, Thailand, Laos, Cambodia, Vietnam, Malaysia, Singapore, Brunei, Indonesia, Timor-Leste, and the Philippines.
Includes resources related to India, Afghanistan, Pakistan, Bangladesh, Nepal, and Bhutan, Sri Lanka, and the Maldives.
Library of Congress subject headings are slow to change despite perpetuating euro-centric, colonial, and often racist stereotypes. At present, "West Asia" as a search term will not locate many resources. Instead, library systems use terms such as "Near East" or "Middle East" in addition to using the names of countries or geo-historical terms such as Saudi Arabi, Iran, Iraq, Jordan, the Levant, etc.
Use the names of individual countries when you want your search to be more specific.