2 Kings 2:11 say
And Elijah went up by a whirlwind into heaven.
But John 3:13 say
And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven.
Did John forget about Elijah?
According to Vincent's Word Studies in the New Testament, Vol. II, "ascended" in John 3:15: "Equivalent to hath been in. Jesus says that no one has been in heaven except the Son of man who came down out of heaven; because no man could be in heaven without having ascended thither" (italics in the original).
It appears that Jesus' emphasis was not the trip to heaven, but being in a place of heaven that only He has entered. I don't know where Elijah ended up, but it evidently wasn't in the same localized area where Jesus was.
There is a vast difference between ascending and being taken up. Taken up as in the case of Elijah means that he was taken to Heaven by another power, in this case by a whirlwind. To the contrary when Jesus ascended it was own power.
So John's statement is correct both Elijah and Enoch were taken to heaven alive:
Genesis 5:24 KJV And Enoch walked with God: and he was not; for God took him.
but only Jesus did it by himself.
Heaven has multiple meanings: the atmosphere/sky, the realm of the stars, and the abode of God.
What Jesus is speaking of in John 3 is about "heavenly things," in reference to God. He says that no one has been with God in heaven (to understand the "heavenly things") except the Son of Man (himself). The kind of closeness that Jesus is talking about is something that no human has experienced.
John 1:18 (NASB)
No one has seen God at any time; the only begotten God who is in the bosom of the Father, He has explained Him.
This is the unique position to which Jesus refers in John 3.
The word translated "heaven" in 2 Kings 2:11 is
8064) which can mean all three of these things. When Elijah was taken up into heaven, he was taken up into the sky. The statement might imply that he was "with" God in some sense, but not in a different way than Enoch (Ge 5), and probably not in a different way than any other righteous person who has died. It is certainly not overtly implied that he has become as intimate with God as deity is with himself.
The following is a Bible based answer. This is what Jehovah's Witnesses believe.
Your question is a great case for letting scripture interpret scripture. The word translated heaven can refer to all or part of the physical heavens including the earth's atmosphere, outer space, etc. (Genesis 27:28, Proverbs 30:19) It can also refer to the spiritual heavens of God's presence which is also where the angels live. Which of these definitions was meant in 2 Kings 2:11? It must be the atmospheric heavens in which windstorms occur, otherwise it would contradict John 3:13. Is there any other evidence that Elijah only went to the sky and if so what was the outcome for Elijah? 2 Chronicles 21:12 indicates that Elijah was still alive on the earth after this since he continued to serve as a prophet. Therefore, after the miracle was over with, Elijah had been relocated to a new location on the earth.
In reality, there is nothing in the Scriptures to show that a heavenly hope was held out to God’s servants prior to the coming of Christ Jesus. Heavenly life was not intended to be the primary hope for faithful humans. (Psalm 115:16) Much of this information comes from the section on Heaven in Insight on the Scriptures. If you want help putting this all into context please see Lessons 5, 6, and 7 from the brochure "Good News From God!".