Did you have acid reflux before starting the hrt, or are you thinking hrt caused it? What type of hrt were you on? Oral is possibly worse for reflux as it goes through your tummy, but it is also a really common symptom during peri and menopause in general.
How is your diet? You may need to go back to a really bland diet for the short term, avoiding potential reflux triggers like spicy food, citrus fruit, tomatoes, alcohol, caffeine, chocolate, maybe even dairy. Important to find out what your personal triggers are as what effects one person might be fine for someone else.
I hope you feel better soon. Search through threads here, reflux comes up a lot!