Based on my experience as a caseworker administering Food Stamps and AFDC/TANF...unless something major has changed in the last couple of years....

Food Stamps & TANF are federal programs, defined by state policy, but administered by the county you live in, so you will have to reapply in that county. Make sure you close the case in your current state and ask for a proof of closure with the effective date on it. Failure to do so could delay benefits, or cuase denial for having an active case elsewhere. Getting an advance appointment is a very good idea. Have all your paperwork together when you go - makes it much quicker and makes a happy caseworker. There is also usually an option of expidited benefits as long as you meet the income and resource criteria.

SSI & Medicaid should transfer as they are federally administrated.

Best of luck!

edited to add....Cases can be transferred from county to county within a state with relative ease. There are some initiatives that have been floating around to make interstate transfers possible. but based on the last knowledge I had that hasn't happened yet.