I think that is pretty much dependent upon how tight your wrap is. Some here can take all kinds of pills pretty much right away. I'm not one of those people. When I tried to take larger-size pills they inevitably got stuck and created discomfort and irritation.
Have you tried opening your omeprazole and dumping them into applesauce? You can't chew them, but they'd be pretty swallowable in that form. They'd taste okay, too.
I still can't take huge pills, and tend to try to get my docs to prescribe smaller versions of whatever they're giving me, and I'm 3 years post op. Others here don't have this problem.
I take (very tasty) liquid calcium, and all my meds are on the small side. I could never take those huge vitamin or supplement pills I used to.
If I were you, I'd wait until the swelling has subsided before trying any big pills. I'm sure others will be by who can give you the other side of this issue. Many here don't have the same problem swallowing pills post-op. Still, you have to consider the possibility that you might be someone who needs to take care.