I fast travel, it loads, screen comes up, I either decide to switch the gun I'm carrying, OR I had holstered my gun so now I'm pulling one out.

But nothing happens. I press and press all the numbers, and no guns emerge. I can move, just can't pull out a gun.

Within about 30 seconds, I can finally pull out a gun. Occasionally I'll hit a stage where I just put up my hands as if there was a gun there, but it's invisible. It always eventually works.

I'm on the PC. Does this happen to anyone else?

This happens all the time for me but is not related to fast travel. Sometimes my gun just won't pull out for up to 10 seconds, which is deadly when in combat.