I'm new to this wiki so I don't know if this has been proposed before but here goes
Ok so we know a few things about this prince that was promised:
1) He/she will come from the line of Aerys II and Rhaella
2) He will fight the great Other
3) Is probably known as Azor Ahai in the East
4) Somehow related to the red comet
My theory is that Jon Snow is actually the promised prince.
He is actually the son of Rhaegar Targaeryen and Lyanna Stark. The promise Lyanna forced Eddard to keep was to raise him as Eddard's son as she knew he would be in danger if his true parentage came out.
If Aegon VI was born under the red comet just a few days before the Sack of Kings Landing then it stands to reason that Jon was too.
It also explains why Melisandre keeps seeing Jon in the fire everytime she searches for Azor Ahai.
And also Lyanna's death. She was weak as she had just given birth.
Thoughts? Let me know if anything is still unexplained or if this theory covers anything I missed
Edit: I'm assuming Jon will live through the stabbing.