Have you tried supplementing Betaine Hydrochloride? As strange as it might seem, heartburn and acid reflux can actually be caused be LOW stomach acid. The stomach needs to be extremely acidic to digest protein, but if food isn't digested properly then it can come back up, and what little acid there is will then cause heartburn.

Low stomach acid can be due to lack of salt or zinc, for example. The chloride in sodium chloride is needed to make hydrochloric acid. Zinc is necessary to make it too. It's possibe this could be linked to the vaccine, if it put a strain your immune system and caused your body to use up more zinc.

But supplementing Betaine Hydrochloride can help produce hydrochloric acid too.

I'm not a doctor, though, and I can't say what's happening with you specifically. Worth looking into, though.