Well first of all, there is always gravity from everything, nothing in the universe isn't effecting you right now (however small the pull might be.)
But to answer your question, time doesn't go slower when you are moving faster, time always goes the exact same speed. It's only when you compare times that you find a difference. You could be traveling half the speed of light and your time would tick the exact same time as someone else who has another clock of identical structure (from each others perspective.) But if you were to look at their stationary clock while you were traveling half the speed of light, it would appear to be moving slower. It also works vica versa.