The Gemara in Baba Basra, Tes Zayin Amud Beis says Reb Shimon says that Avraham had a stone that he wore around his neck that healed the sick. If so why did he need a angel to come down to heal him (Rashi Bereshit 18:2)?
The Gemara there is discussing verse 24:1:
א. וְאַבְרָהָם זָקֵן בָּא בַּיָּמִים וַי־הֹוָ־ה בֵּרַךְ אֶת אַבְרָהָם בַּכֹּל:
- And Abraham was old, advanced in days, and the Lord had blessed Abraham with everything.
The different Rabbis are giving different interpretations how Avraham was blessed.
This didn't happen until after Sarah passed away, which was 37-38 years after Avraham's circumcision.
So a simple answer would be that Avraham didn't use the stone to heal himself after his circumcision because he did not possess it yet.