Uh, no. For quite some time the Nile even flowed west to the Atlantic out the mouth of what is now the Niger (ground penetrating radar from the Shuttle exposed the connecting channel McCauley, 1982). At that time, Lake Chad was the size of the Caspian Sea.
There was a time earlier in its history that what is now the Nile had a canyon deeper than the Grand Canyon. When the Mediterranean flooded, that canyon became a sea inlet (from fossil remains drilled in the current channel). There may have been a geophysical volcanic event near the Bayuda Volcanic Field that diverted it back into where it runs today.
Unfortunately, the paper I'm citing is on JSTOR, so there's no copy directly available online.
Do you have approximate dates on some of this information? 1) When Nile flowed out of the Niger? 2) When Lake Chad was the size of the Caspian Sea? 3) When the Med. flooded creating a Nile sea inlet? 4) When the geophysical even near the Bayuda Volcanic Field may have occurred?
History, technically speaking, means recorded human history, so in practical terms, I was talking about stone age through modern Egypt, at least prior to the Aswan dam.