Each industry is assigned a NAICS (North American Industry Classification System) code. Many databases, search engines, and government websites allow you to search by this code.
You may also need the NAICS Supersectors, which are aggregates for sectors and their industries.
To find a list of companies, use NexisUni (formally LexisNexis). Click "Company Dossier" then "Create a Company List" tab. Then use the NAICS lookup feature to select your NAICS code and click the red create box.
Shift-share analysis looks at multiple peices of information: employment growth nationally, employment growth nationally in an industry, and employment growth locally in an industry are a few data points you can find throught the Bureau of Economic Analysis.
Input and output data is released by the Bureau of Economic Analysis in the form of make and use tables.