I am a licensed RN, NP, PA from out of state and would like to inject during a hands on training, do I need an Illinois license?

Yes hands on injecting now requires a valid Illinois licensure or temporary license through endorsement. This can take up to two weeks to process so apply right away. To obtain a temporary license through endorsement here is a guide:
Go the State of Illinois web site to apply https://online-dfpr.micropact.com/
Click on New Applications and click on the "Click here" button
Register as an Individual. Ensure Yes is checked at the bottom of the application
They will require you to enter SSN to locate whether you have had an account before
Create an account and enter you details
You can now create an Application from the ONLINE SERVICES menu (top right hand side)
If you are a RN and NP choose Nursing Board (RN, LPN & APN). If you are a PA choose Physician Assistant Board
For application method choose Endorsement
Complete the application. Please note that date when its approved to ensure you have it prior to your hands on training event.
Is Illinois a compact state?
The Nursing Licensure Compact (NLC) allows licensed nurses around the U.S. to work in other states that take part in the compact with just one license, called a multistate license. As of September 2022 Illinois is pending for a compact state. Check this website for current information. See more here https://nursejournal.org/resources/nursing-compact-states/