Doctor Who Theory? River and the Fez?

I came up with a theory yesterday. What if River Song is the Fez? What is The Doctor found a Gallifreyan-made Fez in his wardrobe, which was actually a Time Lord whose regeneration cycle has gone horribly wrong? So, he wore it. The Fez's existance ultimately ended with River shooting the poor thing into a series of confetti-like fabric swatches. But. BUT. The fez, which as we had established, was actually a Time Lord, regenerated. Into River Song. So, River (AKA Regenerated Fez) goes and has a series of adventures in which she meets The Doctor. Then comes the day when Eleven finds the Fez in his wardrobe and wears it. River sees the Fez (AKA herself) and realizes that she must shoot the fez, therefore starting her regeneration cycle so events can proceed as they would normally have done. River shoots the Fez, thus completing the time paradox.