I get awful heartburn too, its not nice!! I went to the doctor in the end and they prescribed me with Omeprazole, it stops the stomach producing acid and works really well if I take it just as I am getting up. It does tend to wear off in the early evening so I have gaviscon advance for then. It has made such a difference to me, I would definitely recommend going to your dr for some help, there's no point suffering and its safe to take during pregnancy!
I didnt find anything to help ease it to be honest and I do get it normally but it got so much worse this pregnancy! Hope this helps x