Both my kids had reflux as babies. My daughter was given Axid, we were told it's the same as Zantac (which my son took) but without the alcohol content. Well, it didn't work. She was also given prevacid, but it works completely different than Axid/Zantac. We pretty much demanded she be put back on Zantac (dr didn't think it would make a difference) and it worked.
In my experience, they are given an acid neutralizing medicine first (Zantac/Axid) before an acid production reducing medicine (prevacid).
If you try the Axid and it doesn't work, request Zantac before trying another med.
As for side effects, I know they sound scary but we never had a problem with anything, and I've never heard of anyone experiencing any. The only side-effects from a reflux med I've heard of is from Reglan, which I refused for both my children.
I don't know any herbal meds, but I do know some give I believe it's Mylanta? instead of prescribed meds. Maybe someone here can help with that.
Good luck, it takes patience to find the right med and right dosage sometimes.