Definitely initiate a fraud alert with one of the credit bureaus. They'll immediately do the same for you at the other two. File a police report with your home jurisdiction, which depending what state you are in, should allow you to get a 7-year credit alert for free. The initial alert they give you expires after (I believe) 90 days. You can decide after that if you want to go with the full credit freeze (requires a pin to "thaw" and is more of a PITA) instead of the credit alert (no pin, theoretically more vulnerable to further fraud without it).
You'll want to follow up with the FTC (they collect a database of identity fraud), the SSA (here you're looking for income in your name that you didn't create - unemployment or otherwise, though this only gets updated once a year), the IRS (though don't expect any action from the IRS unless a tax return has been filed in your name). Really, don't expect any of them to do much of anything, but filing the reports create a paper trail that you can refer back to if needed later.