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)?
Rav Moshe Feinstein explains in the Darash Moshe that Avraham could have just prayed to be healed. The reason why he did not is because he loved the pain of the mitzvah. (Whatever that means.)
The Gemara there is discussing verse 24:1:
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.