Jesus does not promise to take away all your troubles. He promises those will get worse. But, Jesus does promise to free you from worry and anxiety.
How does that work?
The Bible says, Be anxious for nothing... (Philippians 4:6) Why? When you trust Jesus, no matter what happens in this life, you will spend eternity with God... and that is VERY GOOD.
And do not be afraid of those who kill the body but are unable to kill the soul; but rather fear Him who is able to destroy both soul and body in hell. - Matthew 10:28
Who can destroy your body and soul? Only God. (Not Satan) However, God does not send you to hell, you do that when you disobey God. However, God created hell, aka. the lake of fire, the second death (Revelation 21:8).
You can be rescued. Jesus Christ (God) died on the cross to save all those who believe in Him... all those who trust Him to pay their just penalty for disobeying God.
Trust in Jesus and you'll know your time on earth is like a wisp of smoke that vanishes in the wind. Trust that Jesus did pay YOUR penalty for sin. Repent. Turn away from disobeying God.
Believe in the Lord Jesus and you will be saved. (Acts 16:31) and there will no longer be a reason for worry or anxiety.