Ideally, the only thing you would grieve for as a missionary would be the sins of the world.
When the resurrected Lord spoke to the three Nephite apostles who desired to remain upon the earth and preach the Gospel until His Second Coming, He told them that in doing so, they would not feel any pain or sorrow “save it be for the sins of the world” (3 Nephi 28:9).
However, you are not one of the so-called Three Nephites.
And you probably have a lot to worry about in your personal and family life, or having to do with your friends, your career, your education, your community, your country, that thing on the back of your leg, etc.
Remember what Mormon told his son Moroni, who was working to preach the Gospel among their people, the Nephites, who had grown extremely wicked:
“My son, be faithful in Christ; and may not the things which I have written grieve thee, to weigh thee down unto death; but may Christ lift thee up, and may his sufferings and death, and the showing his body unto our fathers, and his mercy and long-suffering, and the hope of his glory and of eternal life, rest in your mind forever” (Moroni 9:25).
You will surely suffer when you try hard to do missionary work, because not everyone will accept the messages that you share.
When you feel weighed down, seek to draw near to the Lord in prayer, and let Him lift your spirit and bless you with good cheer.