I own a home in North Carolina and my ex-girl friend is on the deed ?? can she force me to sell the home without me ?? i have had the loan for over 4 years ??

Well I am assuming you are tenants in common meaning you both have 50% ownership of the property but you are 100% liable on the mortgage. Theoretically, she can sell her half ownership in the home, but if you two are breaking up and some kind of property division is going on, she probably could go to court and ask the court to order the sale of the home with proceeds after paying off mortgage and costs of sale being split. But if there would be no proceeds and she might end up having to pay, she may feel differently.