When I touch my face, my hands get a trace of oil from it. Will my hands become impure if I touch someplace impure with these hands? Thanks.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu`alayhi wa sallam, is His slave and Messenger.

You may be afflicted with some kind of whispers, so if this is actually the case, you should strive against these suggestions and seek to get rid of them. As for the question, your hand does not get impure if it touches something impure unless the hand or the item it touched is wet. As such, if both the hand and the item are dry, the impurity could not be moved to the hand. In addition, if you are doubtful whether your hand is wet or not, the original ruling is that it is not wet. Similarly, if you doubt whether or not the impurity has been moved to you, the original ruling is that it is not moved. But, if you realized that your hand was wet and that it got impure because of the item it touched, you have to wash your hand by pouring water on it, which is sufficient to get it purified.

Allah knows best.