When a baby is born, the doctor may ask if you’d like to have your baby circumcised. If this is the case, it happens before they leave the hospital. This is where that time frame comes in. Otherwise, circumcision is “recommended” within the first two weeks after birth.
Here is a medical reason at birth: https://www.cdc.gov/ncbddd/birthdefects/hypospadias.html
Any medical condition after birth that requires a circumcision, needs to be performed by a doctor who knows exactly what they’re doing. Not every doctor does. So you end up with not-so-great stories shared around.
Edit: You describe the tight foreskin you experienced which is in the second link I provided. It is a medical condition that doesn’t require circumcision. In fact, you could still have your foreskin right now. The condition usually goes away over time. Believe it or not. Circumcision is an easy way out. But one that may cost. And in the case of that individual, it did.
Skin is an elastic organ. If you start putting on fat, your skin stretches. The foreskin can be stretched with regular motion. Retracting it on a daily basis would encourage it to stretch. Infections occur only when the foreskin isn’t cleaned well. I don’t know your circumstances personally. Teaching you how to keep clean and retracting the skin is a viable method. I’m not discrediting your parents. Just sharing the logic behind why circumcision is not absolutely necessary or should be the first choice. If this was the informed decision they made for you, I’m glad it was successful with no complications. That’s the best possible outcome.