My state return was supposed to be around $500 and I only received $100. However, I haven’t paid my personal property tax for my car yet. Would the IRS just take that out of my taxes?

The IRS and State Governments have the ability to offset a refund to pay for certain past due debts.  You generally will receive a letter stating what the offset was for.  

The IRS provides a toll-free number, (800) 304-3107, to call for information about tax offsets.

The IRS does not pay state tax refunds.  You need to contact your state tax department.  If you really already filed your state tax return and got your refund (that's pretty amazing this early) then the state will have to tell you why they reduced your refund.  

The IRS has a fairly limited list of items that can be used to offset a federal refund.  The items that can be used to offset a state tax refund will depend on your state's tax laws.