This is a known bug that's typically due to hotkey issues. Do you have hotkeys (1, 2, 3, etc.) assigned for your guns? Often when using these hotkeys to pull a gun out, this occurs. There are a few temporary solutions to it. Zooming out to third person and then back in to first person sometimes helps. Alternatively, selecting the weapon in your Pip-Boy usually works. You can also press F to bring up a mini menu and then use WASD to scroll through the menu and E to select a gun from it. This last option is usually what I try first.
This is an issue that I'd really like to see fixed in the next patch. There are times I'll switch guns with a hotkey and it'll take 10-15 seconds to pull it out. This can be a real problem when I've got a behemoth or a deathclaw running at me lol