One way which has worked for me -- but this of course depends on the severity of your condition -- is adding cream. Not milk but full fat coffee cream.
This dilutes your coffee a little bit, and suppresses any sour or overly bitter notes. Personally I like it even better than coffee without it because you get the softer coffee flavours that might usually be over powered in a standard coffee.
I would also ask why the caffeine is important to you? Regular consumption doesn't improve one's concentration as the body normalises to it.
I would consult your doctor and seek their advice. Acid reflux can be just a mild irritation and easily managed but it can lead to more complicated issues -- such as Barrett's oesophagus. If you are that sensitive to caffeine you might want to leave it alone, or, restrict yourself to decaffeinated drinks.
There is a good question, with answer, here on the subject of brewing coffee with a lower acid content. It seems cold brew coffee could be the way to go!