Definitely sounds like reflux
I get this something shocking when I'm not even pregnant. So far this preg I've managed to keep it under control (with the Rani tablets someone already mentioned) but in the last week they are not working as well as the acid is so bad I feel like being sick
Reni tablets or Mylanta tabs work well if it's mild, these are OTC at the chemist and fine during pregnancy.
If that doesn't work I would get some Zantac or ask your doc for a script for Rani tabs (same thing). I took them right through my DD's pregnancy they are safe.
I know many people don't like to take medication when pregnant but ignoring reflux can cause some nasty damage to your oesophegus and you don't want that either