You need to monitor all of your accounts carefully to make sure that there are no unauthorized withdrawals. In that way, if there are, you can report them immediately to your bank and credit card company and not be liable.
You can also call any one of the three credit reporting bureaus and put a fraud alert on your credit history to prevent a scammer from opening up other bank or credit accounts and taking out loans in your name.
When you do this, any one of the three bureaus will alert the other two and you'll be able to get a full credit report automatically from each of them. You'll be able to see if any of your loans and cards are unauthorized and get that taken care of and cancel any cards or accounts which were compromised.
A fraud alert is free for 90 days, and it means that if, during that time, anyone attempts to open up a card or an account or take out a loan in your name, you will get a phone call before any such loan or credit line gets authorized. After 90 days, you can continue the service for a fee, or you could subscribe to company such as Lifelock, which will do that for you as well.
A fraud alert will not affect your credit negatively. It is only to protect you, and it won't change the way you can use your credit card or bank accounts. It just alerts new lenders not to approve new lines of credit without contacting you first, so that nobody else can use your names and details to get credit and stick you with the payments.
I'm linking you to Experian, because I have the link handy.
The other two are Equifax and Transunion. Again, they all perform the same service and any one will notify the other two. Shortly thereafter you'll also get a copy of your credit history from each of the 3 reporting agencies. And you can get another free copy of your credit history down the road to make sure there's still nothing wrong going on by going to www.annualcreditreport.com.