The idea of hell is in the Bible. The quotes below are King James Version; it is more poetic than most if not all others, and is in the public domain, so anyone can freely quote it. Here are a few examples (there are more, but this should be more than enough to make the point):
Matthew 13:
49 So shall it be at the end of the world: the angels shall come forth, and sever the wicked from among the just,
50 And shall cast them into the furnace of fire: there shall be wailing and gnashing of teeth.
Matthew 18:
8 Wherefore if thy hand or thy foot offend thee, cut them off, and cast them from thee: it is better for thee to enter into life halt or maimed, rather than having two hands or two feet to be cast into everlasting fire.
9 And if thine eye offend thee, pluck it out, and cast it from thee: it is better for thee to enter into life with one eye, rather than having two eyes to be cast into hell fire.
Matthew 25:
41 Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:
Mark 9:
43 And if thy hand offend thee, cut it off: it is better for thee to enter into life maimed, than having two hands to go into hell, into the fire that never shall be quenched:
44 Where their worm dieth not, and the fire is not quenched.
45 And if thy foot offend thee, cut it off: it is better for thee to enter halt into life, than having two feet to be cast into hell, into the fire that never shall be quenched:
46 Where their worm dieth not, and the fire is not quenched.
47 And if thine eye offend thee, pluck it out: it is better for thee to enter into the kingdom of God with one eye, than having two eyes to be cast into hell fire:
48 Where their worm dieth not, and the fire is not quenched.
Luke 16:
22 And it came to pass, that the beggar died, and was carried by the angels into Abraham's bosom: the rich man also died, and was buried;
23 And in hell he lift up his eyes, being in torments, and seeth Abraham afar off, and Lazarus in his bosom.
24 And he cried and said, Father Abraham, have mercy on me, and send Lazarus, that he may dip the tip of his finger in water, and cool my tongue; for I am tormented in this flame.
25 But Abraham said, Son, remember that thou in thy lifetime receivedst thy good things, and likewise Lazarus evil things: but now he is comforted, and thou art tormented.
Revelation 14:
10The same shall drink of the wine of the wrath of God, which is poured out without mixture into the cup of his indignation; and he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb:
11And the smoke of their torment ascendeth up for ever and ever: and they have no rest day nor night, who worship the beast and his image, and whosoever receiveth the mark of his name.
Revelation 20:
10And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.
11And 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.
12And 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.
13And 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.
14And death and hell were cast into the lake of fire. This is the second death.
15And whosoever was not found written in the book of life was cast into the lake of fire.
Notice in that in Revelation 20:10, the torment is explicitly stated to be eternal.
So, the Christian source of belief in hellfire and eternal damnation is the Bible.
But, here is why you should not be afraid. There is absolutely no reason to believe that the Bible is true. It was written by primitive and barbarous people long ago, who were ignorant of how the world works. The book resembles other ancient texts of other primitive people, full of all sorts of things that are now known to be impossible. The people who believe this sort of thing are people who have been indoctrinated into such beliefs as children.
One of the interesting things is how even most people who believe such primitive superstitious twaddle, would reject the exact same stories if they were told in a contemporary setting. For example, if your fiancée told you she was a virgin, but she was pregnant, would you believe her? If not, why would you believe the same story in an ancient book, when you don't know who wrote it, and there is no proof that the story is true, or even any reason to believe the story is true?
With a book, it can claim absolutely anything, and need not have any connection to the truth.