Nope, kinematic time dilation is symmetric. Your watch is running slow compared to theirs from their perspective and theirs is running slow from yours.

Similarly, there is no way to say which one of you is stationary and which is moving at 0.995c, because you are both justified in saying you are the stationary one and the other person is moving. Motion is relative and there is no absolute motion or sense of absolute stillness.

One complication: due to kinematic redshifting/blueshifting you may observe the other person’s clock as running slower (if they are moving away from you) or faster (if they are moving towards you) than the time dilation calculation would predict, but that’s just an apparent effect. When they are moving right by you you will observe only the time dilation itself, and you will still find the time dilation present at all times when you account for the apparent kinematic effects.