I've had this - mercifully without the lips turning blue. Dd (5 in July) fell and hurt her head recently. Cried then within seconds went floppy and limp with eyes rolling back in her head. I shook her and screamed and she came too and started crying hysterically.
Same thing happened last week when she collided with a door. Again I screamed in terror and shook her and she came to.
Mum reminded me that as a small child I would black out if the pain was too much in precisely the same way. Apparently it happened a few times - once when I fell down stairs, once when I twisted an ankle, and once when I fell awkwardly and a sharp stone cut and lodged in my knee.
So it could just be a faint. However tbh the blue lips thing is concerning......check it out with GP