The machine at the gym that measures your fat body percentage as well other similar devices is very unreliable since it depends on your body's water content. Your water content in your body can vary greatly depending on whether you just exercise, how much you drank, etc.

There are better but typically more expensive or invasive ways to measure body fat such body fat calipers (devices that measure your fat by pinching it) to something like dual x-ray mass absorption (DEXA) which is highly accurate but somewhat expensive. I do believe it's best to go by how you are feeling and look in the mirror.