For me, it depended a lot on the context and the reason for being naked...
For example, I also started to feel embarrassed at the doctor's office around the age of 11 or 12.
Away from home, I remember the first time I went to the beach when I was about 7. Up until then, I'd been naked (partly out of habit, not because they forced me), and a friend of my stepmom came to visit. She and her daughter, who was a little older than me... I didn't know her very well; we'd played together a few times. Finding myself naked in front of her, in a swimsuit, made me very embarrassed.
At home, I never felt too embarrassed until puberty. But even after that, very little. In fact, I was used to being seen naked from a young age. As I've written in other posts, for health reasons, I've had several enemas, so nudity was also normal.
And even as I grew older, I never felt much embarrassment. As I said, it depends a lot on the context.
One time I felt really embarrassed was when I was about 10, when my stepmother gave me an enema while her sister was present... She wanted to see why she had to do it to her son. She'd certainly seen me naked before as a child, but it had been years, she wasn't someone I knew very well, and I felt helpless.