What to do if I want to break the lease in my low income apartmentsince my household income now exceeds their income restrictions but they won’t let me?

You don't specifically mentioned that you have a lease, but considering that you are trying to "break the lease," I take it that you do have one. A lease is a written contract, which means that what is written in your lease contract controls how you begin and end your lease.   Most Texas landlords will use standardized lease forms which will contain sections that talk about how to end the lease early.  If your contract says that the lease terminates when you no longer meet income guidelines, then you can give the apartment complex notice that you are cancelling per that specific provision.  If your contract says you cannot end your lease early, but if you do you will be subject to certain penalties (like a default of your deposit), you can "break the lease" by giving notice and just moving, but understand the penalties associated with moving early.  If the penalties are too steep, consider just waiting until the lease expires naturally to move.  If this is a government funded program, you may want to talk to the agency that funds the program.  You may have a specific duty to report your higher wages to the agency.  Failure to report you income could result in civil and criminal penalties. Let the agency know that you are not trying to defraud the government, and then request their assistance in dealing with the apartment manager.