Is it impossible to think that after judgment day being thrown into hell and then not existing after that is way worse than being in hell?

Yes there is and it is the Revelation.

Rev 20:11 And I saw a great white throne, and him that sat on it, from whose face the earth and the heaven fled away; and there was found no place for them.

Rev 20:12 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.

Rev 20:13 And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.

Rev 20:14 And death and hell were cast into the lake of fire. This is the second death.

Rev 20:15 And whosoever was not found written in the book of life was cast into the lake of fire.

You might also look at the words of Jesus in:

Mar_9:44 Where their worm dieth not, and the fire is not quenched.

Mar_9:46 Where their worm dieth not, and the fire is not quenched.

Mar_9:48 Where their worm dieth not, and the fire is not quenched.

and if I may I suggest you read the entire 9th chapter of Mark

Does hell really burn forever?

Ask yourself this, are Sodom and Gomorrah still burning? No they are not.

Even as Sodom and Gomorrha, and the cities about them in like manner, giving themselves over to fornication, and going after strange flesh, are set forth for an example, suffering the vengeance of eternal fire.

Jude 1:7

Because they are set as an example of what eternal fire will be like, you can see that they are not burning eternally. The everlasting fire means the fire cannot be quenched. There is no escape. The fire comes from Him who is an All-consuming fire, God Himself.

There are different schools of thought on this, but to me it is evident that hell is not happening right now, and that it is not forever. For many reasons.

1) God is a JUST God.

If a man were to enter a store and steal something, would it be fair for him to receive life in prison? Definitely not. The punishment does not fit the crime. In the same manner, God will not punish those who living a sinful life of 70 or 80 years with millions, billions, or trillions of years of burning. The punishment does not fit the crime.

2) The story of the rich man and Lazarus is a parable.

The rich man and Lazarus is surrounded by parables. In Luke 15 Jesus tells the story of the prodigal son, a story that is accepted as a parable. In the beginning of Luke 16 He tells the parable of the rich man and his dishonest manager (which as you can see starts the same way as the rich man and Lazarus). Then the parable of the rich man and Lazarus.

It would be too lengthy to get into the specifics of why Jesus said that parable and its meaning, but I'll out a resource at the bottom. Just a couple of things. If you take the parable of the rich man and Lazarus as reality, then you must accept that people who go to heaven go to Abraham's physical bosom and people who go to hell can be seen by those in heaven and can even speak to them.

3) Pain in the new heavens and the new earth

After the Earth is recreated (new heavens and new earth), there will be no more sorrow, pain or suffering. If you believe in an eternal hell, there will still be sorrow, pain, and suffering.

4) Destroy both body and soul

The eternal suffering in hell is made under the presumption that we 'have an immortal soul'. How can the soul be immortal if it can be killed? These are contradictory and I choose to believe the Bible and the direct words of Jesus when He says,

And fear not them which kill the body, but are not able to kill the soul: but rather fear him which is able to destroy both soul and body in hell.

Matthew 10:28

These are just a few reasons but there is an overwhelming amount of evidence that hell is not burning right now, that it will not be eternal, and that the soul is NOT immortal. It you wish to know more about what the Bible says about this visit this website.

Also, if you'd like to watch a short video on this, it can be found on this website, or here.

EDIT: A sermon explaining this topic from the SCRIPTURE ONLY can be found here.