So, I went to my doctor and he said: I have microtear on my Achilles tendon or insertional Achilles Tendonitis. The pain is on the backside of the heel. And so, it feels like the pain is coming from the heel bone, not the tendon. He explained how the tendon fans out and wraps around the heel bone closer to the foot. And as you said, excessive loading and lack of stretching before and after badminton can aggravate the situation. Age does not help too when you get older. He prescribed me anti-inflammatory medication to be taken the next 10 days and asked me to do some heel stretches. It is much better now. The pain is not 100% gone especially after badminton, but it is much better. I am now taking more precaution with stretching the heel before and after badminton.
For anyone still reading this post, I used to have pain at back of my heel. I managed to fix it with 2 things 1. A pair of better shoes (this could be just my misconception or coincidence but the pain got better around same time I had this new shoes) 2. Stretch and relax all muscles and tendons that are at back of leg, above ankle. For me, even though the point of pain was near heel area, the cause really was muscles/tendons up above being too tensed. I use massage gun to loosen them up after each game, and the pain is completely gone. It used to bother me for a few years, and I had tried many other things to no avail.
Recently had this issue (plantar fasciitis), the solution is stretch, stretch, stretch even on days you are not playing.