Your thoughts are certainly normal, as your wife and friends tell you, but I don’t completely agree with their approach to “just ignore it”.
First of all, we are taught in Ethics of the Fathers (3:1): Akavya ben Mehalalel said: Reflect upon three things and you will not come to the hands of sin. Know from where you have come, to where you are heading, and before Whom you will give justification and accounting. From where have you come — from a putrid drop; to where are you heading — to a place of dust, worms and maggots; and before Whom will you give justification and accounting — before the King Who reigns over kings, the Holy One, may He be blessed.
Contemplating our past existence in this world, our future inevitable death in this world, and our eternal existence with potential reward of immeasurable dimension in the next world is a vital part of understanding that our life has meaning, a plan and a purpose.
Let me share a story with you. Rabbi Yosef Chaim Sonnenfeld, the Rav of Jerusalem until 1932, told people that every single day after his fortieth birthday he would contemplate his passing from this world. When his students suggested that that sounded somewhat morbid, Rabbi Sonnenfeld answered them that it was not true! He explained that in order to be able to keep a balanced approach to this world and the next world it is necessary to know that one's time on this world is finite and needs to be used to the fullest.
Perhaps this might be an approach to remove any fear that you feel. Not to look at your feelings and thoughts as something negative, but rather as an awakening that will allow you to utilize your time here to the fullest, and in the most spiritually satisfying way possible. May you and your family share much happiness, good health and success together for many, many years to come.