Reflux and sleeping issues. Please help!

Im a first time mom with twin boys that are almost 3 months old. They absolutely refuse to lay on their backs and in at a loss of what to do. They spit up constantly when laid down on their backs and end up choking and it shoots out their nose. Their arms spring up and they get frantic. Ive tried letting them clear their airway by themselves but dont seem to do it. I freak out and will sit them up so they can breathe, but i thought they are suppose clear it themselves? They'll literally flail around for more than 10 seconds and I can't sit there and watch them choke. They will only sleep in their twin z pillow and I have to watch them or be close because the pillow is not advised for safe sleep because of a suffocation hazard. Ive tried so many times to lay them flat, but they choke every time. Ive brought it up to their pediatrician and she said it may be reflux and to try to lay them on their sides or get a incline wedge, but everyone says those sleeping methods are dangerous. I keep them upright when feeding as well as keep them upright for 30 minutes after feeding. I burp them half way through their bottle and when they're finished. I give them gas drops when they're gassy. I feel like a bad mom for not knowing how to help them or ease their discomfort and feel like i tried everything. It breaks my heart to see them like this. I didnt sleep last night because everytime I put them down they would spit, choke and scream. What am I doing wrong??