Talk to a bankruptcy attorney in SC. If you only debt is the mortgage, then filing bankruptcy depends on whether the lender will seek a deficiency against you. If you have lots of other debt, bankruptcy would make sense regardless of the mortgage deficiency likelihood. In any event, the foreclosure process would take some time, during which you could live in the home rent free until it is over. If you are going to NC anyway, and do not need to stay in the home, you could offer the lender a deed in lieu of foreclosure, making sure that it waives the right to any deficiency claim. The attorney would also be able to advise you re protecting your disability benefits.
Filing bankruptcy at this point is premature, unless you have significant other debt that would make it a good idea. In SC, it will take 3-6 months for a foreclosure to complete, and longer if you choose to fight it or request a loan modification as part of the foreclosure intervention process. If that is long enough for you to make your move, and you don't want to fight it, then allowing the foreclosure to proceed may make sense for you. Once you get the foreclosure papers, look in the Complaint (normally on the first page) to see if it says Deficiency Waived or Deficiency Not Waived. If the deficiency is waived, then they just want the house back, and won't try to get a judgment against you for any money owed to them after foreclosure. If they do get a deficiency judgment against you, that would be a good reason to consider filing a bankruptcy.