And Hashem appeared to him in the field of Mammre and he was sitting at the entrance of the tent in the heat of the day.
Rashi explains; And Hashem appeared to him: to perform the mitzvah of bikkur cholim (visiting the sick).
Rebbi Chama ben Chanina said: It was the third day from his circumcision, and Hakodosh Baruch Hu, came and inquired about his welfare.
Zera Shimshon asks in the name of the Mefarshim why Rashi prefaced Rebbi Chama ben Chanina's statement by saying that Hashem came to Avraham in order to do the mitzvah of visiting the sick? Why couldn't Rashi simply say that Hashem came to Avraham because this was the third day after Avraham did a bris milah and we would understand that Hashem came to make a bikkur cholim visit?
Zera Shimshon answers in light of Tosafos who asks; Chazal teach us that until Yaakov there was no sickness in the world! When it came time for a person to die he simply died. If so, Tosafos asks, how can it be that Hashem came to do bikkur cholim with Avraham? Tosafos answers that only natural illnesses did not exist until Yaakov, however, sicknesses that resulted from wounds from knives and the sort did exist.
Zera Shimshon explains that this is exactly the intent of Rashi. Meaning, after Rashi explained that Hashem came to visit Avraham who was ill, Rashi asked himself, how can that be, sickness didn't exist yet in this world? Rashi therefore cited Rebbi Chama the son of Chanina that Avraham circumcised himself and sickness from such an action did exist.
What still has to be understood, though, is how did Rebbi Chama ben Chanina derive that it was the third day after Avraham's milah? Where is there even a slight allusion in the Parsha that this happened on the third day and not the first, second, or tenth day?
To answer this question, Zera Shimshon asks another question. Avraham wasn't the only person that got circumcised on that day. Yishmael and Avraham's servants also did milah that day. Why then did Hashem only come to visit Avrohom and not the rest of the people who had circumcised themselves with Avrohom?
Zera Shimshon answers this in light of the Gemara in Babba Basra that Avrohom wore around his neck a special stone that had the power to immediately heal anyone who looked at it. According to this, explains the Zera Shimshon, all of the other people who circumcised themselves with Avrohom looked at the stone and immediately were healed. By the time Hashem came they were all better and therefore there was no need to visit them.
Avrohom, on the other hand, didn't want to go this route. Chazal teach us, "according to the pain so is the reward". Avrohom was totally focused on the World to Come and he didn't want to lose any potential reward.
Another reason that Avraham didn't want to heal himself sooner was Avrohom knew this was a test to see if he was totally obedient to Hashem's will, if he healed himself right away, people would say that he listened to Hashem and circumcised himself only because he knew that it really wasn't dangerous since he knew how to cure himself! (Would it be a big deal if Houdini was put in a box underwater with an oxygen tank?) Avrahom therefore opted to "sit tight" and wait for the circumcision to naturally heal.
According to this we can explain the reason Hashem did not come to heal Avraham (which is a part of of the mitzvah of bikkur cholim) on the first or second day after the Milah. People would say the only reason why Avrohom circumcised himself is because he knew the pain wouldn't last too long and they wouldn't realize that Hashem was the One that healed him and it wasn't that he looked at his special healing stone. People would say that Avrohom wasn't totally subservient to the will of Hashem and he would not do ANYTHING Hashem commanded him, for instance if it was hard. Therefore, Hashem waited to visit and heal him on the day that he would naturally heal to show that Avraham was happy to do whatever Hashem commanded him to do even if he had to endure great pain to do it.
(We can understand another reason for Avrohom not looking to lessen his pain in light of the Missilas Yesharim's (chapter 19) description of someone who truly loves Hashem, ".... The more deterrents that cross their path for people who truly love Hashem...the more will their hearts fortify themselves and rejoice to show the strength of their faith, just as a military leader, who is famous for his strength will always throw himself into the heart of the battle, where a victory will serve all the more to reveal his prowess. It is common that every lover of flesh and blood rejoices in a situation that he can show how far his love goes- Sh. P.)