My hands and feet are swelling and staying that way. What could cause this? I have high blood pressure and don't eat a lot of salt

Any number of things. Can cause peripheral edema. Probably most common is medication side effect, followed by congestive heart failure. You need to see a doctor for definitive diagnosis and treatment, because this could be something serious.
Swelling hands-feet. There are many possibilities. Swelling may be related to sleep apnea, heart problems, kidney problems or to menopausal hormone problems. You need to make an appointment for a check up with your doctor to sort this out and help you.