As you suspected you have acid reflux
Normally lower end of food pipe (oesophagus) called cardia made of ring of muscle fibre opens while food passes down to stomach and soon after that it closes and remains so till next time food passes down. This prevents the stomach contents with gastric juice(acidic) flowing up the food pipe.
increases intra-abdominal pressure causing cardia to open. So the stomach contents are pushed up, sometimes up to throat and even spill over to voice box. This causes irritation there inducing cough
While lying down the pull of gravity is eliminated. So stomach contents can easily flow upwards.
So keep the head end of bed up by elevating that side of cot itself making it to slant and not by keeping pillows.
Take frequent meals but small quantity especially before going to bed.
Avoid bending forwards (increases pressure inside abdomen)
With these measures if your symptoms persist you may take an antacid
Even with this if your problem persists see an ENT specialist
or a Gastroenterologist
Wish you good health