You will never officially be diagnosed with perimenopause. There is no test and many doctors still think it's all in our heads or stress
Coughing never worked for me. It did with the run of the mill heart palps I used to get occasionally. But these relentless, strong ones I was having all day everyday for months, coughing did nothing. Belching did seem to make me feel better too but they would never stop. You have a vegas nerve that runs parallel to your esophogus and goes to the stomach. I think the flopping of the heart being so close to that nerve as well causes the urge to want to burp. My GP prescribed blood pressure meds to see if it would stop the heart palps. It didn't stop them.
I mentioned I went to a hormone doctor. She prescribed progesterone for me and that didn't even make them go away. Only time and my body's own adjustment to whatever was happening in my body made them go away.
You might have some estrogen dominance and that could be what's causing the heart palps. I read that you can do things to help your liver more efficiently break down the excess estrogen. Eating a salad with dandelion greens is supposed to help the liver better clear the excess. Might be something to consider. I started exercising more vigorously. I began biking about 20miles per day at least 4 times per week. I noticed the biggest improvement when I started that. Exercise will of course cause your body to function better and that in turn will help it respond better to the constant fluctuation of hormones we are subjected to in our late mid-late 40s.
I'm sure your blood work will come back fine. If you have an EKG I'm sure it will be fine. You could probably have all of the heart tests I had (twice) and everything came back fine. Just like so many of us. Do push for more tests if you are concerned because the stress won't help them go away. But I'll bet dollars to donuts your heart is fine and healthy.