I've always been on prescription prilosec. The Flight Doc told me I'm cleared hot to take it daily, prilosec no longer requires a waiver if it is taken for acid reflux. That's what he wrote the presciption for... and what I do.
I've been flying for 20 years, taking prilosec for the last 7. I took it no more than 3 times a week to avoid needing the waiver. A waiver was required for taking it daily until about 2 years ago but is no longer required for prilosec. I'm not sure if initial entry is any different or nexium vs prilosec but I bet your chances are good.