完治したって英語でなんて言うの？

You can use "I'm all better" to express that any medical ailment (wound/injury/illness/surgery) has healed.
In the case of a broken leg, it could go something like this:
A: Hey, man. I see you got your cast off.
B: Yea, thanks. I'm all better now.

You could also say "I'm back to normal." What you are basically saying is that whatever ailment you had is gone and your body has returned to how it was before.

If you've recovered from an injury (怪我), you can say that you're "as good as new." It means that you're back and even better than before.

You could also say, "I am completely back to normal now." This means that you are just doing everything you usually do without and discomfort or inconvenience. You could also say, "I'm better now."
A "How is your broken leg?"
B "It's better now.'
A " What do you mean? Are you walking already?
B " Yes, it's completely healed up now. I have totally recovered!"

Recovered = (of a person) cured, healed, or having regained health after an illness

Example :

He is fully recovered from the virus.

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When a broken bone or other injury heals or when something heals it, it becomes healthy and normal again.

Example :

Within six weeks the bruising had gone, but it was six months before it all healed.

To recover from an accident may take time...
But the body is a remarkable & self-repairing system and many injuries heal faster than we might imagine:-)
I am fully recovered /completely cured, indicates you are "back to your old self"
or back to 100% fitness

*I have fully recovered from the leg injury.
A: Sam you are back at work already!
B: Oh yes, I have completely recovered now.

*The wound has completely healed. - This shows that a wound has healed and maybe only a scar is left. A scar is a mark that shows that there was a wound or cut.