Welcome to the forum, maybella1213.
Why did you stop the medicine your doctor prescribed? Did the cold, if it was that, go away? Lemon and honey aren't going cure an infection, just maybe feel good. The codeine promethazine was for the cough. Did your cardiologist say to stop that? There isn't anything that cures a cold. But if the condition goes on for a time, it's more than a cold, and that's why the doctor would prescribe an antibiotic.
You mentioned getting tachycardia out of the blue. I get it too, but it's not out of the blue. I have a specific sensitivity to a chemical that brings it on. I didn't have it all my life; it's acquired.
My sensitivity happens to be to sulfites, but others have reactions to different chemicals. Sulfites are preservatives in things like dried fruits, bleaching agents in things like boxed or canned potatoes, and are used in the processing of corn into corn starch. And that's just for a start. They're natural in a few foods.
To find out if one has a sensitivity, my allergist has people keep a food diary/log/journal. We write down everything we eat or drink, all medications, and the time. Then we also write down any reactions, for me the tachycardia, especially within 2 hours. People who get migraines have to look back as far as 2 days to find the trigger food.
If you get a list of possible trigger foods, you then google the list and "food allergies." That's how I found my whole list and what is in those foods.
I don't have any tachycardia now, as long as I don't consume sulfites above my tolerance level. It's not like a peanut allergy. It's called a sensitivity now.
There are loads of threads on food sensitivities and sulfites. Just put some words in the search box at the top of the page.