Hmmm . . . I'm not sure I buy that, but let's play with this. First, a question: From earth, you would appear to be slowing down, whereas from your vantage point, earth's activities (her clock) would appear to be accelerated, wouldn't they?
No, each would observe that the other's clocks had slowed down. So it would always be, unless the ship decelerates, turns around, and accelerates toward earth again. Then you have a situation where the ship's clocks have been through some motions that earth had not experienced. This gets complex, and I'll rely on Physicist to go into detail (as I always do when I'm over my head). When the ship gets back to earth, it becomes obvious that it's only the ship's clocks that had slowed down.